Solutions to Self-Test Exercises

Chapter 11 Capital Budgeting 11-3

CHAPTER 11

capital budgeting

SOLUTIONS TO SELF-TEST EXERCISES

Self-Test exercise 11.1:

traditional payback period

The Millers are considering a $200,000 expansion for their existing retail outlet. The expansion would generate $35,000 in cash each year over the next 10 years. Calculate CompuTech’s payback period.

Payback period

$200,000$35,000=5.71 years

Self-Test exercise 11.2:

payback reciprocal

A retailer is interested in selling a retail business to the Millers for $1 million. This includes all physical assets, the working capital, and goodwill. The Millers estimate, based on the company’s historical financial statements that the annual cash inflows would be around $195,000. Calculate the project’s payback reciprocal.

Payback reciprocal

$195,000$1,000,000=19.5%

Self-Test exercise 11.3:

net present value

Using the information in Self-Test Exercise 11.1, and assuming that CompuTech’s weighted average cost of capital is 8%, calculate the project’s net present value.

Net present value using the 8% discount rate:

Cash outflow $( 200,000)

Present value ($35,000 × 6.7101) $234,854

Net present value $ 34,854

Self-Test exercise 11.4:

net present value: purchase of existing business

Use the information in Self-Test Exercise 11.2, and assume that the Millers want to make 20% on their investment and would like to sell the retail store for $4 million in the 20th year. Calculate the company’s net present value, and calculate the net present values by using the following discount rates: 18%, 19%, 20%, 21%, and 22%.

Net present value using the 20% discount rate:

Cash outflow $(1,000,000)

Present value $(195,000 × 4.8696) 949,572

Sale of store $(4,000,000 × 0.02608) 104,320

Total present value 1,053,892

Net present value $ 53,892

For each incremental percentage, the net present value is as follows:

NPV @ 18% = $189,808

NPV @ 19% = $118,012

NPV @ 20% = $53,892

NPV @ 21% = $( 3,565)

NPV @ 22% = $( 55,282)

Self-Test exercise 11.5:

internal rate of return

Use the information in Self-Test Exercise 11.1 to calculate the project’s internal rate of return.

Use the payback period as a factor (see answer to Self-Test Exercise 11.1) and go to Table D in row 10. By crossing the discount columns, reach the factor that is closest to 5.71 which is at 12% (5.6502).

Cash outflow / $ (200,000)
Cash inflow ($35,000 × 5.6502) / $197,757
Net present value / $ ( 2,243)

To calculate the IRR, you have to multiply the $35,000 amount by a factor using a discount rate that is slightly less than 12%; to be exact, the rate is 11.73%.

Self-Test exercise 11.6:

internal rate of return

Use the information in Self-Test Exercises 11.2 and 11.4 to calculate the project’s internal rate of return.

As shown in Self-Test Exercise 11.4, the rate that makes the inflows equal to the outflow is between 20% and 21%, closer to 21%. By interpolation, or using a financial calculator, the internal rate of return gives exactly 20.93%.

Self-Test exercise 11.7:

profitability index

Use the information in Self-Test Exercises 11.1 and 11.3 to calculate the profitability index.

By using the information obtained in the NPV calculation in Self-Test Exercise 11.3 divide the discounted cash inflows (8%) by the cash outflows.

$234,854$200,000=1.17

Self-Test exercise 11.8:

profitability index

Use the information in Self-Test Exercises 11.2 and 11.4 to calculate the profitability index.

By using the information obtained in the NPV calculation in Self-Text Exercise 11.4, divide the discounted cash inflows (20%) by the cash outflows.

$1,053,892$1,000,000=1.05

Self-Test exercise 11.9:

buy versus lease option

Questions

If the Millers want to make 30%, should they buy or lease the retail store? To answer this question, calculate the following:

1.  Net present value

2.  Internal rate of return

Option A: Purchase

1. Net present value: At 30%, the net present value is $104,033.

2. Internal rate of return: The internal rate of return is 33.84%.

Option B: Leasing

1. Present value: At 30%, the present value is $170,492 ($70,000 × 2.4356).

2. The IRR cannot be calculated since there is no cash outflow.

Since the leasing option offers a greater NPV, it would be more economically advantageous to lease. Also, leasing is considered less risky than buying and there is no cash outflow and no financing would be required.

Self-Test exercise 11.10:

project analysis

These are the numbers that were presented in the opening case on page 463.

Calculations

Factors Factors Factors

Years @ 11% PV @ 20% PV @ 25% P.V.

0 (350) -- (350) -- (350) -- (350)

1 (25) 0.9009 (23) 0.8333 (21) 0.8000 (20)

2 5 0.8116 4 0.6944 3 0.6400 3

3 100 0.7312 73 0.5787 58 0.5120 51

4 125 0.6587 83 0.4822 60 0.4096 51

5 140 0.5934 83 0.4019 56 0.3278 46

6 150 0.5346 80 0.3349 51 0.2621 40

7 150 0.4817 72 0.2791 42 0.2097 31

8 150 0.4339 65 0.2326 35 0.1678 25

9 150 0.3909 59 0.1938 29 0.1342 20

10  150 0.3522 53 0.1615 24 0.1074 16

10  900 0.3522 317 0.1615 146 0.1074 97

Net present value 516 133 10

Questions

1. What is CompuTech’s NPV using 11% and 20% weighted average cost of capital?

At 11% is $ 516,046

At 20% is $ 132,688

At 25% is $ 10,295

2. What is the retail store’s payback period?

Payback is 5.03 years

3. What is CompuTech’s IRR?

The internal rate of return is 25.52%.

4. What is the PI?

Using the 11% cost of capital ($516,000 + $350,000 = $866,000)

$866,000$350,000=2.47

5. Should the Millers go ahead with the opening?

Yes. The Millers should go ahead with the decision because the cost of capital is 11% and the hurdle rate is 20% while the project gives a 25.5% IRR.

© 2014 by Nelson Education Ltd.