Discounted Cash Flows and WACC In Class Practice Exercises
and Answers (ungraded)
- Calculate the future value of $100,000 invested today for 20 years at 16 percent.
- What is the total present value of the following cash stream, discounted at 20 percent?
Year Amount
1700
2700
3565
4322
5 3,578
- You invest 4,320 per year for each of the next 15 years. Your investment yield per year is 8 percent. How much money do you have at the end of 15 years?
- Please calculate the present value of the following cash stream: 550 dollars received annually for 20 years and 210 dollars received immediately. Your discount rate is 12 percent.
- Your rich uncle gives you a proposition. If you give him 500 dollars today. He will guarantee your receive 10 percent a year for the next 10 years. How much money will you receive from him at the end of 10 years?
6.Your company wants to buy a refurbished replacement backhoe for 22,000 dollars. You can get 17,000 when you sell your current backhoe The life of a backhoe is about 10 years in your business. You anticipate to save the following in maintenance charges over the next ten years: year one: 1,500; year two: 1,250; year three 1,249; year four 1,000; year five: 310; year six 1,200. After year six you anticipate no maintenance savings. What is the NPV of this proposal? Should you make this investment if your required return is 10 percent?
Note: These WACC exercises are very similar to the homework assignment. Please follow the format from these practice exercises when doing your homework this week.
7. You have collected the following information:
a. the yield on your company’s preferred stock 5%
b. the yield on your company’s debt 7%
c. the required return on your company’s common stock and internal equity 9%
d. debt total $15,000,000
e. preferred stock current market value $15,000,000
f. common stock and retained earnings total value $40,000,000
Please calculate the pre-tax weighted average cost of capital (WACC) for your company.
8. Your company’s marginal income tax rate is 35%. Please calculate the post tax WACC from the information provided in problem one.
Discounted Cash Flows and WACC In Class Exercises Answers
Please note that different DCF tables may have slightly different multipliers due to rounding differences when the algebraic formulas were applied.
1. Calculate the future value of $100,000 invested today for 20 years at 16 percent.
This is a problem using the future value of one dollar table. You have a single number (100,000) that is received today and invested for twenty years. You want to find the value of this investment at the end of the twenty-year period.
N=20 I= 16% FV of $1 table
19.461 X 100,000 = 1,946,100
2.What is the total present value of the following cash stream, discounted at 20 percent?
Many discounted cash flows problems have dissimilar cash flows projected out into the future, similar to the list below. You use the present value of one dollar table for each calculation. You utilize the same interest rate (20 percent) but a different period (n =1 or n=2 etc) for each calculation. Then you add all of these present values up to get the total present value of the cash stream.
If we were determining whether or not to invest in a “widget machine” and these cash flows represented the future savings from using this machine, we would then net the total present value of these cash flows against the initial negative investment (the dollars that we spend to buy the “widget machine”.)
Year Amount PV of $1 Table Present Value
1700 X .8333 = 583
2700 .6944 = 486
3565 .5787 = 327
4322 .4823 = 155
5 3,578 .4019 = 1,438
Total PV 2,989
- You invest 4,320 per year for each of the next 15 years. Your investment yield per year is 8 percent. How much money do you have at the end of 15 years?
This is an annuity since we will invest a equal number of dollars each year and the investment is consecutive for 15 years. We use the future value of an annuity table for our calculations.
N = 15 I = 8% FV of annuity table
4,320 X 27.152 = 117,297
- Please calculate the present value of the following cash stream: 550 dollars received annually for 20 years and 210 dollars received immediately. Your discount rate is 12 percent.
Again, this is an annuity. However, we want to know the value today of this annuity (whereas in problem three we wanted to know the value of the annuity in the future). So we will use the present value of an annuity table.
Period 0 1 2 3 ………….. 20
210 550 550 550 ……….. 550
PV of future
Cash stream 4,108 7.4694 X 550
@ n= 20
I = 12%
PV of Annuity ------
Total Present Value 4,318
5.Your rich uncle gives you a proposition. If you give him 500 dollars today. He will guarantee your receive 10 percent a year for the next 10 years. How much money will you receive from him at the end of 10 years?
This is a future value problem because you want to know how much money you will receive in the future, if you make an investment today of 500 dollars. The language in this problem is a bit confusing since you will receive 10 percent a year. This does not mean you will receive cash payments each year equaling ten percent. It states that your investment, when mature, will have resulted in a return of ten percent each year.
Since only one cash flow is involved (500 dollars invested today or period zero) then you use the future value of one dollar table.
Period 0 1 2 3 ………….. …..10
500
Future Value of $1 500 X 2.5937 = 1,297
N= 10, I = 10%
- Your company wants to buy a refurbished replacement backhoe for 22,000 dollars. You can get 17,000 when you sell your current backhoe The life of a backhoe is about 10 years in your business. You anticipate to save the following in maintenance charges over the next ten years: year one: 1,500; year two: 1,250; year three 1,249; year four 1,000; year five: 310; year six 1,200. After year six you anticipate no maintenance savings. What is the NPV (Net Present Value) of this proposal? Should you make this investment if your required return is 10 percent?
This is a typical capital budgeting type problem. You have an initial investment (which is negative since it is a cash outflow at period zero). And you have a forecasted savings stream which is variable cash flow. Savings represent avoidance of cash outflows, so they are considered positive numbers.
You use the present value of one dollar table to calculate the present value of this cash stream. It is done in the same manner as in problem one.
Although the net savings are provided in this problem, in real life you would have had to calculate the actual maintenance savings, by comparing the cost of keeping the backhoe versus the cost of buying the new one. If the Annual maintenance costs of the present backhoe were 3,000 per year and the new backhoe’s maintenance costs were expected to be 1,800 per year, you would calculate the net savings (1,200 per year) and discount the 1,200 back to the present value to compare it against the initial investment.
Initial Investment - (22,000) + 17,000 = (5,000)
Period 0 1 2 3 4 5 6 7 8 9 10
Initial Invest (5000)
Annual Net 1500 1250 1249 1000 310 1200 0 0 0 0
Cash savings
PV of $1 table .9091 .8264 .7513 .683 .6209 .5645
@ 10% 1364 1033 938 683 192 677
Total PV 4887
------
NPV (113)
Since the Net Present Value (NPV) is negative, you are not receiving your required return. Therefore you would not make this investment.
7. You have collected the following information:
a. the yield on your company’s preferred stock 5%
b. the yield on your company’s debt 7%
c. the required return on your company’s common stock and internal equity 9%
d. debt total $15,000,000
e. preferred stock current market value $15,000,000
f. common stock and retained earnings total value $40,000,000
Please calculate the pre-tax weighted average cost of capital (WACC) for your company.
Answer:
$ % Total Pretax Yield Avg. Yield
Debt 15,000,000 21.4% X 7% = 1.50%
Preferred Stock 15,000,000 21.4 X 5 = 1.07
Common Stock 40,000,000 57.2 X 9 = 5.15
& Retained Earnings
------
Total $70,000,000 100% 7.72% WACC (Pretax)
8.. Your company’s marginal income tax rate is 35%. Please calculate the post tax WACC from the information provided in problem one.
Answer:
Debt enjoys a tax benefit. It is reflected in a lower yield since interest payments are considered expenses and shield some sales income from taxation.
Debt Post Tax Yield Calculation:
Pretax Yield 7%
Marginal Tax Rate 35%
Calculation:
7% x (1 - .35) = 4.55% post tax yield on debt
$ % Total Posttax Yield Avg. Yield
Debt 15,000,000 21.4% X 4.55% = .97%
Preferred Stock 15,000,000 21.4 X 5 = 1.07
Common Stock 40,000,000 57.2 X 9 = 5.15
& Retained Earnings
------
Total $70,000,000 100% 7.19% WACC (Post tax)