Question

Q1

a) You will receive $1,000 from your parents as a birthday gift in half year. You have decided to invest it at 5% per annual until you have $1,629. How many years will you have to wait from NOW until you achieve your target?

b) You will receive fifty annual payments of $1,000 each beginning at the end of the 40th year. What is the present value of these payments? The appropriate annual discount rate is 10%.

Q2

a) A bond of 10 years maturity is left with 8 years to maturity today. Its coupon rate is 10%, paying annual coupon with par value of $1,000. What is the price of the bond today if the yield to maturity is 8%? Is it a premium bond or discount bond?   

b) Recently, a 30-year corporate bond issued by Liz Co. has been downgraded by a credit rating agency from AAA to B. Other things being constant, what would you expect to happen to the price and yield of the bond as a consequence of the downgrade?

Q3

LogiTel Corp. is a public company which had issued both common stock and cumulative preferred stock. In its recent meeting, management has decided not to pay dividends in the next 3 years.

a) John, a shareholder of LogiTel, is unhappy with the management’s decision and intends to sue the company for not paying dividends. Briefly comment on John’s intention.

b) Briefly explain the cumulative feature of preferred stock.


c) Assume that LogiTel will pay a dividend of $1 per share of common stock at the end of year 4. Dividends are expected to grow at 5% per year in year 5 and 6. After that, dividends will growth at a constant rate of 1% per year indefinitely. Calculate the current common stock price if the required return is 8%.

Answer 1

1.

a.

P = $1000

r = 5%

A = $1629

We know formula for Amount after compound interest is

A = P * (1+ r ) ^ n

1629 = 1000 * (1.05) ^ n

1.629 = (1.05)^n

By trail and error,

n = 10.00132584

n = 10 for practical purposes

So it will take 10.5 years to achieve the goal.

b. We will receive $1000 for next 50 years starting from ending of 40 years. So this payments will be made till the end of 90 years.

P = $1000

r = 10%

n = 40

Here there are two times discounts to be applied. One is the present value of future annuity at 40 years at 10% and then again discount that present value for 40 years at 10%

Thus applying the formula of PV of Annuity

PV =

= 1000 * ((1-(1.1)^-40)/0.1)

= 1000 * (9.7790507185)

= 9,779.0507185

= 9779.05

Now we have to discount the value of $ 9779.05 for 40 years to get its present value today

P or FV = 9779.05

r = 10%

n = 40 years

PV = FV /(1+r)^n

  = 9779.05 /(1.1)^40

= 216.0674071466

= 216.07