Question

6. (PV) You have just joined an investment bank. The company offers you two different salary arrangements. You can have $50,000 per year for the next 3 years or $30,000 per year for the next 3 years, along with a $50,000 signing bonus today. If the market interest rate is 16%, which salary arrangement do you prefer?

7. (EAR and Nominal Interest Rate) An investment will increase in value by 270% over the next 17 years. What is the annual interest rate which, when compounded quarterly, provides this return?

8. (Perpetuity)A firm invests $3 million in a project which will yield a perpetuity of $1 million per year. What is the discount rate r for which this project’s present value is $4.5 million? 9. (Amortization) You just bought a car with loan of $50,000. You have to repay the loan in 6 years with monthly payments. The interest rate on the loan is 4%.

a. What is your monthly payment?

b. How much will you still owe after 4 years? (i.e. what is the loan balance after 4 years?)

Answer 1

6.

Discount rate	16.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
-	0	-	-
50,000.000	1	43,103.45	43,103.45
50,000.000	2	37,158.15	80,261.59
50,000.000	3	32,032.88	112,294.48

Option A PV = 112,294.48

Discount rate	16.0000%
Cash flows	Year	Discounted CF= cash flows/(1+rate)^year	Cumulative cash flow
50,000.00	0	50,000.00	50,000.00
30,000.000	1	25,862.07	75,862.07
30,000.000	2	22,294.89	98,156.96
30,000.000	3	19,219.73	117,376.69

Option B PV = 117,376.69

so second option is better

7. EAR = ((1+2.70)^1/4 - 1 ) * 4 = 154.77%

8. present value of perpetutiy = 3 + 4.5 = 7.5 million

rate = 1/7.5 = 13.33%

9. PV = 50,000, FV = 0, rate = 4%/12, N = 72

use PMT function in Excel

a) monthly payment = 782.26

put N = 48 and calculate FV

b) amount owed after 4 years = 18,014.06