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Finance questions- Time Value of Money, Bonds, NPV

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1. Mr. Miser, who is 35 years old, has just inherited $11,000 and decides to use the windfall towards his retirement. He places the money in a bank which promises a return of 6% per year until his planned retirement in 30 years. If his funds earn 6% interest compounded annually, how much will he have at retirement? Repeat the analysis for both semi-annual and continuous compounding.

2. An investment today of $3,300 is worth $10,000 in 8 years. At what rate has your investment been growing (annually) over the 8 years?

3. Joe, a freshman in college, needs $55,000 in 4 years to buy the car of his dreams. If his investments earn 6% interest per year, how much must he invest today to have that amount at graduation? If he invested once a year for four years beginning today until the end of the 4 years how much must he invest?

4. As the winner of the Housecleaners sweepstakes, you are entitled to one of the following prizes:

A. $999,999 immediately.
B. $100,000 per year forever.
C. $180,000 per year for the next 10 years starting immediately.
D. $400,000 payable every 2 years over 20 years.
E. $ 70,000 per year forever.

5. Your aunt, in her will, left you the sum of $5,000 a year forever with payments starting immediately. However, the news is better. She has specified that the amount should grow at 5% per year to maintain purchasing power. Given an interest rate of 12%, what is the PV of the inheritance?

6. If you invest $100,000 today at 12% per year over the next 15 years, what is the most you can spend in equal amounts out of the fund each year over time.

7 . Given the following set of spot rates: Year 1: Spot Rate= .050; Year 2: Spot Rate = .054; Year 3: Spot Rate = .059; Year 4: Spot Rate = .066. Calculate the 1-year forward rates over each of the next 3 years.

8. Given the opportunity to invest in one of the three bonds listed below, which would you purchase? Assume an interest rate of 7%.

Bond
Face Value
Annual Coupon Rate
Maturity Price

A
$1,000
4%
1 year $990

B
$1,000
7.5%
17 years $990

C
$1,000
8.5%
25 years $990

9. The Walker Landscaping Company can purchase a piece of equipment for $3,600. The asset has a two-year life, will produce a cash flow of $600 in the first year and $4,200 in the second year. The interest rate is 15%. Calculate the project's Discounted Payback and Profitability Index assuming steady cash flows. Should the project be taken? If the Average Accounting Return was positive, how would this affect your decision?

10. The NPV and Profitability Index give the same results when there is no conflict. In the case of capital rationing, explain the potential conflict and the way it should be solved with supporting examples.

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The solutions provides answers to Finance questions on Time Value of Money, Bonds, NPV.

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Beta, present value, Net Present Value, Time Value of Money, Bonds, YTM, discount rate

15. If a firm has a beta of 1.0, it is safe to make the following conclusion regarding the relative risk of the firm to the market risk in general:

a. The firm is about as risky as the market.
b. The firm is more risky than the market.
c. The firm is less risky than the market.
d. The beta of the firm does not allow any conclusion about relative risk.

16. Which of the following cash flows has the highest present value for all rates of interest greater than 0%:

a. $100 per month for a year
b. $1200 immediate payment
c. $50 every two weeks for a year
d. They all have the same present value.

17. A proposed project can generate savings of $1000 per year for 10 years. The initial cost of the project is $2500 and the project has a salvage value of $500 in the 10th year. What is the Net Present Value of the project to the nearest dollar if the discount rate is 10%?

a. $7000.00
b. $3644.00
c. $3451.00
d. $3837.00

18. If current interest rates on savings are 5% and you can save $300.00 per month toward the down payment on a house, how long will it take you to save for the down payment if the minimum down payment amount is $20,000.00?

a. 5.55 years
b. 5.00 years
c. 4.91 years
d. 6.00 years

19. The coupon rate of a bond is 12% and the bond has a par value of $1000.00. What is the annual interest payment received by the bondholder:

a. $120.00
b. $60.00
c. $1200.00
d. $12.00

20. Which of the following statements is not true:

a. When the YTM of the bond is equal to its coupon rate, the bond will sell at its par value.
b. If the coupon rate of a bond is lower than the current YTM of the bond, the bond will sell for more than its par value.
c. The par value of a $1000.00 face value bond is $1000.00.
d. The value of a bond moves in the opposite direction as its YTM.

21. Which is the proper factor to use when computing the present value of an annuity of 100 monthly payments with a discount rate of 12% per year?

a. PVIFA(100,12%)
b. PVIFA(100,1%)
c. FVIFA(100,12%)
d. None of these

22. All of the following factors are important in determining the appropriate discount rate for a project except:

a. The firms weighted average cost of capital.
b. The Debt position of the firm.
c. The risk profile of the typical investor in the firm.
d. The level of risk associated with the project

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