FI3300: CORPORATE FINANCE
Problem Set 1 Chapters 6-9
1. What is the real rate of interest?
a. the nominal rate of interest
b. the actual return after inflation
c. the coupon on a bond
d. the inflation rate
2. A saving account that pays a 10% stated interest rate p.a. has the highest future value if it exhibits ______compounding.
a. Yearly
b. Semiannually
c. Quarterly
d. Monthly
3. The yield to maturity of a bond is the same as which of the following?
a. the interest rate
b. the coupon
c. the price
d. all of the above
4. What is a zero coupon bond?
a. a fixed income investment with no payments until maturity
b. a bond with a coupon that has a zero on it
c. a bond with the same yield as its coupon (zero difference)
d. a and c are true statements
5. You recently sold some stock your parents purchased for you in 1981 (25 years). You received $12,717.63. Your parents paid $2,000. What was the average annual return?
a. 7.68%
b. 8.53%
c. 6%
d. $10,717.63
6. You just deposited $4000 into a bank account paying 5% compounded semi-annually. How much money will you have after two years?
a. $4,202
b. $4,400
c. $4,415
d. $4,862
7. Assume an interest rate of 8%. You are indifferent between receiving $5,000 in 4 years or $______today.
a. 3,402.92
b. 3,969.16
c. 3,756.57
d. 3,675.15
8. Assume a deposit of $1,000.00 is worth $2,000.00 in eight years. The interest rate on the account was _____%.
a. 4.05
b. 6.05
c. 8.05
d. 9.05
9. A deposit of $2,315.25 will become $3,257.79 in ___ years. The account earns 6%.
a. 4.86
b. 5.36
c. 5.86
d. 6.36
10. The value at time 0 of receiving $1,000 per year beginning in year fifteen and ending in year thirty is $______. Assume a 6% interest rate.
a. 10,105.90
b. 5,380.99
c. 4,469.85
d. 3,120.40
11. The value at time 0 of $400 per year forever with the first payment received in exactly one year is $______. Assume an interest rate of 10%.
a. 4,000.00
b. 4,333.33
c. 4,444.44
d. 4,555.45
12. Assume you borrow $300,000 to buy a house. You commit to making monthly payments for 30 years. The rate on your loan is 6.000%. After 200 monthly payments you owe $______to your mortgage company.
a. 173,234.51
b. 145,689.23
c. 175,456.89
d. 197,770.54
13. Assume a bond pays semi-annually, has 5 years to maturity, and has a 7.00% coupon. The discount rate is 8.00%. If the bond has a par value of $1,000 then it should sell for $_____.
a. 1,041.58
b. 1,041.00
c. 960.07
d. 959.45
14. Assume a bond has 10 years to maturity, pays semi-annually, has a par value of $1,000 and sell for $935.00. The discount rate is 9.00%. The coupon rate of this bond is _____%.
a. 3.5
b. 5.0
c. 4.0
d. 8.0
15. A firm just paid a dividend of $2.00 next year. The required rate of return is 11% and dividends are expected to grow at 6% forever. The stock should sell for $______.
a. 69.80
b. 38.10
c. 40.00
d. 42.40
16. The common stock of Darkover Inc just paid a dividend of $2.00 per share. The dividend is expected to grow at a constant rate forever. The required rate of return for this stock is 10%. If the current price is $30.00 then the expected growth rate is ____%.
a. 3.125
b. 5.000
c. 7.125
d. 9
17. A firm expects dividends to grow at 20% for the next two years and 5% thereafter. The firm just paid a dividend of $1.50 and the required rate of return is 10%. The stock should sell for $______.
a. 36.86
b. 37.86
c. 39.86
d. 40.91
18. Which of the following is a correct statement?
a. a bond with a 9% coupon will sell at a premium if the yield to maturity is less than 9%.
b. bonds are similar to preferred stock because owners of both can vote
c. bonds are fixed income securities and the price does not fluctuate
d. a bond with a 7% coupon will sell at a premium if the yield to maturity is more than 7%
19. What is the price of a 12% coupon bond with 15 years to maturity and face value $1,000 that is priced to yield 8.5%?
a. 761.62
b. 1000.00
c. 1290.65
d. 2039.88
20. Problem 30 in the book chapter 7 (page 223).
21. An annual annuity payment of $100 for fifteen years would be worth $1,500 today if the interest rate were…
- 0.0%
- 2.5%
- 3.0%
- 10.0%
- impossible to determine with the information provided.
22. You recently made a $25,000 investment in a gem mining partnership. The general partners
said you would receive a 10% return on your investment over the four-year life of the partnership. The estimated cash flows of the investment are indicated below. How much must the partners pay you in year 4 to assure you receive a 10% return?
0 1 2 3 4
-$25,000 $8000 $5000 $0 ???
Find out the NPV assuming a cash flow of 0 at t = 4
CF0= 0, CF1 = 8000, F1 = 1, CF2 = 5,000, F2 = 1, CF3 = 0, F3 =1, CF4 = 0, F4 = 1, I = 10%, NPV = 11,404.96
The PV of cash flow at T= 4 is the difference between cost and NPV, which is (25,000-11,404.96) = 13,595.04
Now find out the FV of 13,595.04 at t = 4
PV = -13,595.04, PMT = 0, 1/Y = 10%, N=4, FV =? 19,904.50
23. If you deposit $4,000 into a Roth IRA annually –that means each year – from age 22 – 55 (33 years), how much will you have if your return is 5%? What if your return is 10%? (8 points)
5%
10%
24. What is the monthly mortgage payment on a 15 year $200,000 loan with an interest rate of 6%? After 10 years how much have you paid in interest?
Monthly Payments
Total Interest years 1 – 10
25. The value in one year (t=1) of receiving $700 per year for 13 years with the first payment beginning in three years (t=3) is ____%. Assume a 6% interest rate.
a. 4,191.92
b. 5,846.11
c. 5,515.20
d. 6,196.88
26. Joe is 25 today. He will make a deposit into a retirement account on his birthday (including today) until he turns 65. The account earns 8%. He wants to withdraw $50,000 per year starting on his 66th birthday and ending on his 85th birthday. How much must he deposit each year?
a. 1,748.36
b. 1,897.98
c. 2,001.25
d. 2,025.36.
This is an annuity due problem.
BGN mode,
N = 20, PMT =50,000, 1/Y = 8%, FV = 0, PV =? 530,179.96 (at t = 66)
N = 41, 1/Y = 8%, PV = 0, FV =530,179.96, PMT = ? 1,748.36
27. You need to pay for your children’s college education. You have triplets that have just had their first birthday. By the time they reach age 18, you feel college will cost $18,000 per year per child or $54,000 per year for 4 years beginning 17 years from now. You plan to have all the money required for the children to complete 4 years of school when they enter college at age 18, which is 17 years from today. How much should you save annually in order to provide this benefit? The required return is 6% throughout. (Use 17 years for the accumulation period and assume the first payment is made in year 17. All regular annuities – no imbedded tricks.) Use this problem as a first step to understand problem #25 of the book, page 222. Once you understand the latter, you can work on the next problem.