Question

Q1/Imprudential, Inc., has an unfunded pension liability of $678 million that must be paid in 17 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 8.7 percent, what is the present value of this liability? (Enter answer in millions. E.g., 100 million goes in as '100'.)

Q2/Assume a bronze sculpture sold in the year 2,010 at auction for a price of $10,424,744. Unfortunately for the previous owner, he had purchased it in year 1,996 at a price of $12,333,689. What was his annual rate of return on this sculpture? (Enter answer in percents, not in decimals.)

Q3/Suppose you are committed to owning a $228,233 Ferrari. If you believe your mutual fund can achieve a 14.76 percent annual rate of return, and you want to buy the car in 10 years on the day you turn 30, how much must you invest today?

Q4/Twenty years ago, you deposited $5,398 into an account. Fifteen years ago, you added an additional $8,009 to your account. You earned 5.68 percent, compounded annually, for the first 5 years and 9.81 percent, compounded annually, for the last 15 years. What is the value of your account today?

Q5/You are expecting to receive $300 at the end of each year in years 3, 4, and 5, and then 500 each year at the end of each year in years 10 through 25, inclusive. If the appropriate discount rate is 6.4 percent, for how much would you be able to sell your claim to these cash flows today?

Q6/You expect to receive 1000 bucks every year at the end of each year, starting in year 7 and ending in year 21. If you expect the rate of return is 10.2 percent, and you invest all your cash flows at the going rate as soon as you receive them, how much money will you have at the end of year 25?

Answer 1

1..Present value of the pension liability=

678/(1+0.087)^17=

164.18

millions

2..

Purchase Price in1996= 12333689

Sale Price in 2010= 10424744

Loss for (2010-1996)=15 years =10424744-12333689=

-1908945

Annual return on the sculpture= (-1908945/12333689)/15=

-1.03%

3.. The amount X to be invested today so that the final amount at end of (30-10)=20 yrs. Will be $ 228233 at an annual rate of 14.76% will be =

228233=X*(1+0.1476)^20=

Solving for X,

X= $ 14540

4..Value of the 1st deposit after 5 yrs. At 5.68% p.a. =5398*(1+0.0568)^5=7115.36

Value of the total deposit(5398+8009) after 15 yrs. Ie. Today at 9.81% p.a.=(5398+8009)*(1+0.0981)^15= 54570.76

So,total value of the account today= $ 54570.76

5..The sale amt. today = Sum of the Present values of all the cash flows discounted at 6.4%

To find the PV of the 1st part,ie.annuity of $ 300 at end of yrs. 3 ,4 & 5

ie.(300/1.064^3)+(300/1.064^4)+(300/1.064^5)=

703.13

Alternatively, can be worked out as

PV of yrs. 3 to 5 , $ 300 cash flows=PV of the $ 300 cash flows till end yr. 5- PV of the $ 300 cash flows till end yr.2

(300*(1-1.064^-5)/0.064)-(300*(1-1.064^-2)/0.064)=

703.13

Working out as in the 2nd method (because tedious to find PV of each $ 500 cash flow )

PV of yrs. 10 to 25 , $ 500 cash flows=PV of the $ 500 cash flows till end yr. 25- PV of the $ 500 cash flows till end yr.9

(500*(1-1.064^-25)/0.064)-(500*(1-1.064^-9)/0.064)=

2813.36

So, sale value today=703.13+2813.36=

3516.49

6.. This involves future value of annuity

Future value annuity for yrs. 7 to 2 = Future value of annuity for full 21 yrs.-FV of annuity for 1st 6 yrs.

Accordingly,

(1000*(1.102^21-1)/0.102)-(1000*(1.102^6-1)/0.102)=

57814

Now, finding the FV of a single sum of $ 57814 for 4 yrs, ie at end of 25 yrs.

57814*(1+0.102)^4=

85263

Money at the end of year 25= $ 85263