Finance questions- Time Value of Money, Bonds, NPV

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.