Question

You can choose to undertake two mutually exclusive projects: Project 1 will return in one year a

payoff of 120 with probability 10%, or a 0 payoff with 90% probability. Project 2 will return in one

year a risk-free payoff of 15. Both projects require an initial investment of 10. You do not have any

money and need to raise it from external debt holders. Assume that everybody is risk-neutral, that

the risk-free interest rate is 0 and that bond holders act competitively.

What is the face value of the one-year maturity zero-coupon bond at which bond holder will be

willing to lend you the 10 amount you need to start the one project you select?

A. 10

B. 60

C. 100

D. 120

The answer is C.

Can anyone help me with the calculation? thank you

Answer 1

here,

the one-year maturity zero-coupon bond at which bond holder will be willing to lend you the 10 amount you need to start the one project, Amount we need is 10 So, investor willing to lend 10 amount means 10* 10 = $100

therefore,

Bond Value =100

rate or yeild = 0

time to maturity = 1 yr

100 = F/( 1+ 0 ) ^1

Face value is 100

Else , if bond price is 10 then face value will also be 10 because if interest rate is 0 the Face value will be equal to bond price.