[cartoonsmart]

Forever working co. has a consol bond that just made a $50 coupon payment, the bond makes annual payments in perpetuity that grow at a rate of 5% every year. Your required return on these consol bonds is 10%.

How much would you pay for this bond today?

If the bond was issued 20 years ago, what coupon payment was made at the end of the first year the bond was outstanding?

If the required return was 12 percent 20 years ago, and forever working issued 1000 of these bonds, what was the company's proceeds from the issuance?

I got stuck, I need a clear workout of this not just the answers, I need to know how this one is done, so thank you for your attention

[reinsuranc]

1. Let P = present value today.

The 50 grows 5% each year, and is discounted to present value 10% each year.

P = 50 + 50*(1.05)/(1.10) + 50*(1.05^2)/(1.10^2) +...

P = 50*(1 + u + u^2 +... ), where u=1.05/1.10 = .9545 approximately

P = 50*(1 / (1 - u) ) = 1,099.


2. Today the coupon was 50. The coupon has been growing 5% each year.
Twenty years ago the coupon was 50/(1.05^20) = 18.84.

3. Twenty years ago, at 12%, the present value was:

P = 18.84 + 18.84*(1.05)/(1.12) + 18.84*(1.05^2)/(1.12^2) +...

P = 18.84*(1 / (1 - u) ), where u=1.05/1.12=.9375; P = 301.44

1000*P = 301,440.