Module 11
Demonstration Problem
Brown Company
Brown Company is considering a project that will have a useful life of 10 years. The initial investment required would be $2,000,000. Each year, the project would generate revenues of $900,000 and expenses of $600,000 (including depreciaton of $200,000). The company’s cost of capital is 12 percent.
Calculate the following: (1) payback period, (2) accounting rate of return, (3) net present value, and (4) internal rate of return.
1. Net income per year = $900,000 - $600,000 = $300,000.
However, this includes depreciation of $200,000.
Depreciation is a non-cash expense.
Annual net cash flows = $300,000 + $200,000 = $500,000.
Payback period = original investment / annual cash flow
= $2,000,000 / $500,000
= 4 years.
2. Accounting rate of return = average income / initial investment
= $300,000 / $2,000,000
= 15%
3. Net present value:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $2,000,000 / 1 / $(2,000,000)
Annual cash flows / 1-10 / 500,000 / 5.650 / 2,825,000
Net present value / $825,000
4. Factor for internal rate of return = initial investment / annual cash flow
= $2,000,000 / $500,000
= 4.00
Looking in the present value of an ordinary annuity table, we see that for 10 periods, the factor is 4.192 for 20% and 3.923 for 22%. Thus, the IRR for the project is between 20 and 22 percent. Interpolation gives the answer to be 21.43%.
Practice Problem 1
Klein Company
Klein Company is deciding which of two machines to buy. Both Model X and Model Y cost $20,000 and have expected lives of 5 years. The estimated net cash inflows are $8,000 each year with model X. However, the estimated net cash inflows with model Y vary each year as follows: Year 1, $7,000; Year 2, $8,000; Year 3, $9,000; Year 4, $10,000; and, Year 5, $8,000. The cost of capital for the company is 12 percent. Which model should the company choose, if the Net Present Value criterion is used?
NPV for Model X:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $20,000 / 1 / $(20,000)
Annual cash flows / 1-5 / 8,000 / 3.605 / 28,840
Net present value / $8,840
NPV for Model Y:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $20,000 / 1 / $(20,000)
Return in year 1 / 1 / 7,000 / 0.893 / 6,251
Return in year 2 / 2 / 8,000 / 0.797 / 6,376
Return in year 3 / 3 / 9,000 / 0.712 / 6,408
Return in year 4 / 4 / 10,000 / 0.636 / 6,360
Return in year 5 / 5 / 8,000 / 0.567 / 4,536
Total present value of cash inflows / $29,931
Net present value / $9,931
Model Y has the higher NPV, and is therefore better.
Practice Problem 2
Cronin Company
Cronin Company has been presented with an opportunity to invest in a new line of business. The initial investment is $500,000, and the company expects to have additional annual cash expenses of $75,000 per year. Depreciation on the investment will be $50,000 per year and additional cash revenues from the new business are expected to be $175,000. Cronin company expects to fund this project with 50 percent debt and 50 percent equity. The cost of capital for debt and equity are 8 percent and 12 percent, respectively. The company is using a ten year planning period, and believes the numbers given above will be constant through the ten year life of the project.
Calculate the following: (1) payback period, (2) accounting rate of return, (3) net present value, and (4) internal rate of return.
1. Annual net cash flows = Additional cash inflows – additional cash outflows
= $175,000 - $75,000
= $100,000
Payback period = original investment / annual cash flow
= $500,000 / $100,000
= 5 years.
2. Cash expenses per year = $75,000
However, this does not include depreciation expense which is $50,000 each year.
So, total expenses are $125,000 ($75,000 + $50,000).
Hence net income per year = $175,000 - $125,000 = $50,000 per year.
Accounting rate of return = average income / initial investment
= $50,000 / $500,000
= 10 %
3. Net present value:
Cost of capital for the project = (0.5 x 8) + (0.5 x 12) = 10 percent.
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $500,000 / 1 / $500,000
Annual cash flows / 1-10 / 100,000 / 6.145 / 614,500
Net present value / $114,500
4. Factor for internal rate of return = initial investment / annual cash flow
= $500,000 / $100,000
= 5.0
Looking in the present value of an ordinary annuity table, we see that for 10 periods, the factor is 5.216 for 14% and 4.833 for 16%. Thus, the IRR for the project is between 14 and 16 percent. Interpolation gives the answer to be 15.13%.
Exercises
Multiple Choice
1.Which of the following statements is false about the payback method?
A. The payback method uses cash flows in evaluating investments
B. The payback method discounts cash flows in evaluating investments
C. The payback period is the time required to recover the initial investment.
D. The payback period is calculated by dividing the initial investment by annual cash flow.
2. Green Company is considering a project that will have a useful life of 10 years. The initial investment required would be $1,000,000. Each year, the project would generate revenues of $400,000 and expenses of $200,000 (including depreciation of $100,000). The company’s cost of capital is 12 percent. The accounting rate of return is
A. 12%
B. 20%
C. 25%
D. 30%
3. Green Company is considering a project that will have a useful life of 20 years. The initial investment required would be $1,000,000. Each year, the project would generate revenues of $500,000 and expenses of $300,000 (including depreciation of $50,000). The company’s cost of capital is 12 percent. The payback period is
A. 2 years
B. 3 years
C. 4 years
D. 5 years
4. Which of the following methods uses net income rather than cash flows in evaluating capital investments?
A. accounting rate of return
B. payback period
C. net present value
D. internal rate of return
5. Which of the following statements is true?
A. The net present value is not a discounted approach to evaluating capital investments.
B. The payback method is a discounted approach to evaluating capital investments.
C. The accounting rate of return is a discounted approach to evaluating capital
investments
D. Discounted approaches consider the time value of money in evaluating capital
investments
II. Matching Problem
C / Estimated average annual net income from the project divided by the average investment / A. Net Present ValueA / The amount by which the sum of the present values of the expected annual cash flows from a project exceeds the initial investment / B. Payback Period
G / Differences in value of equal amounts of cash flows obtained at different times due to compounding of interest / C. Accounting Rate of Return
E / The cost of financing activities through debt or equity is called the / D. Required Rate of Return
B / Period of time in which the initial investment in a project can be recovered / E. Cost of Capital
D / Minimum acceptable return on capital investments / F. Internal Rate of Return
H / Models that consider the time value of money in evaluating capital investments / G. Time Value of Money
F / The interest rate that results in zero net present value / H. Discounting Models
Homework Problem 1
Nixon Company
Nixon Company is considering the purchase of a new machine, which costs $600,000 and has a useful life of 4 years. The company uses straight line depreciation, and the estimated salvage value is zero. The cost of capital for the company is 10%. If the machine is purchased, the additional annual cash inflows will be $600,000 and the additional annual cash outflows will be $400,000.
Calculate the following: (1) payback period, (2) accounting rate of return, (3) net present value, and (4) internal rate of return.
1. Annual net cash flows = Additional cash inflows – additional cash outflows
= $600,000 - $400,000
= $200,000
Payback period = original investment / annual cash flow
= $600,000 / $200,000
= 3 years.
2. Cash expenses per year = $400,000
Noncash expense (depreciation) each year = $150,000 ($600,000/4).
Total expenses = $550,000 ($400,000 + $150,000)
So, net income = $600,000 - $550,000 = $50,000 per year.
Accounting rate of return = average income / initial investment
= $50,000 / $600,000
= 8.33%
3. Net present value:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $600,000 / 1 / $600,000
Annual cash flows / 1-4 / 200,000 / 3.170 / 634,000
Net present value / $34,000
4. Factor for internal rate of return = initial investment / annual cash flow
= $600,000 / $200,000
= 3.0
Looking in the present value of an ordinary annuity table, we see that for 4 periods, the factor is 3.037 for 12% and 2.914 for 14%. Thus, the IRR for the project is between 12 and 14 percent. Interpolation gives the answer to be 12.60%.
Homework Problem 2
Bush Company
Bush Company is considering a project that will have a useful life of 10 years. The initial investment required would be $2,400,000, and the required rate of return is 12 percent. The expected annual revenues and expenses for the project are given below:
Sales / $1,600,000Variable expenses / 900,000
Contribution Margin / 700,000
Fixed expenses / 400,000
Net income / $300,000
The fixed expenses include depreciation of $120,000 per year.
Calculate the following: (1) payback period, (2) accounting rate of return, (3) net present value, and (4) internal rate of return.
1. Total fixed expenses are $400,000 but this includes depreciation of $120,000 per year. So cash fixed expenses are $280,000 ($400,000 - $120,000).
Annual net cash flows = Additional cash inflows – additional cash outflows
= $1,600,000 - $900,000 - $280,000
= $420,000
Payback period = original investment / annual cash flow
= $2,400,000 / $420,000
= 5.71 years.
2. Net income per year = $300,000 per year.
Accounting rate of return = average income / initial investment
= $300,000 / $2,400,000
= 8.33 %
3. Net present value:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $2,400,000 / 1 / $2,400,000
Annual cash flows / 1-10 / 420,000 / 6.145 / 2,580,900
Net present value / $180,900
4. Factor for internal rate of return = initial investment / annual cash flow
= $2,400,000 / $420,000
= 5.714
Looking in the present value of an ordinary annuity table, we see that for 10 periods, the factor is 6.145 for 10% and 5.650 for 12%. Thus, the IRR for the project is between 10 and 12 percent. Interpolation gives the answer to be 11.74%.
Homework Problem 3
Carter Company
Carter Company is considering three possible investment opportunities. The initial investment and annual net cash flows are given below:
Project / Initial investment / Annual net cash flows1 / $100,000 / $30,000
2 / $120,000 / $35,000
3 / $150,000 / $30,000
The cost of capital is 10 percent, and all projects have useful lives of 6 years. Using the NPV method as the selection criterion, rank the projects in terms of their attractiveness.
NPV for Project 1:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $100,000 / 1 / $100,000
Annual cash flows / 1-6 / 30,000 / 4.355 / 130,650
Net present value / $30,650
NPV for Project 2:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $120,000 / 1 / $120,000
Annual cash flows / 1-6 / 35,000 / 4.355 / 152,425
Net present value / $32,425
NPV for Project 3:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $150,000 / 1 / $150,000
Annual cash flows / 1-6 / 40,000 / 4.355 / 174,200
Net present value / $24,200
Based on NPV, the most attractive project is Project 2 because it has the highest NPV; the second-best project is Project 1 while the least attractive project is Project 3.
Homework Problem 4
Johnson Company
Johnson Company is considering three possible investment opportunities. The cost of capital for the company is 10 percent. The investment and annual net cash flows are given below:
(a) Project 1 requires an initial investment of $500,000 and net cash flows are $100,000 each year for 8 years.
(b) Project 2 requires an initial investment of $675,000 and net cash flows are $1,400,000 at the end of 8 years (once only, not every year!).
(c) Project 3 requires an initial investment of $100,000 as well as investments of $140,000 at the end of each year for 5 years. The cash inflows from the project are $150,000 each year for 8 years.
Using the NPV method as the selection criterion, rank the projects in terms of their attractiveness.
NPV for Project 1:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $500,000 / 1 / $(500,000)
Annual cash flows / 1-8 / 100,000 / 5.335 / 533,500
Net present value / $33,500
NPV for Project 2:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $675,000 / 1 / $(675,000)
Annual cash flows / 8 / 1,400,000 / 0.467 / 653,800
Net present value / $(21,200)
NPV for Project 3:
Item / Years / Amount / Present value factor / Present value of cash flowsInitial investment / 0 / $100,000 / 1 / $(100,000)
Annual investments / 1-5 / 140,000 / 3.791 / (530,740)
Annual cash flows / 1-8 / 150,000 / 4.355 / 653,250
Net present value / $22,510
Based on NPV, the most attractive project is Project 1 because it has the highest NPV; the second-best project is Project 3. Project 2 should not be chosen because it has negative NPV.