How did you get:

C$).$ To raise a $$100$ million from the Lenders, the company should promise to pay back the principal as well as interest.

Explanation:

The promised rate should coincide with the expected rate of return on the project that lenders anticipate.

In this case, since Project A has a higher NPV$,$ the promised interest rate should be calculated based on the cash flows of Project A$.$

The promised interest rate can be calculated as:$-$

$100=[150/(1+$ r$\_$d$)1]+100/(1+$r$\_$d$)1$

putting the above values given in the question, we get r$\_$d$=7\mathrm{.}92\%$

And, the expected rate $($r$\_$e$)$ is the risk free rate which is $5\%.$

Sapphire Ltd$.$ is a company where managerial compensation is linked to the value of the firm$$s stock. The company has only two investment opportunities, A and B$,$ and must choose between them. In the case of investment opportunity A$,$ an already established technology would be used, and the project would generate next year $$150$ million with certainty. Project B relies on a brand new untested technology, and as such has only a limited probability of success. A research team at Sapphire Ltd$.$ forecasts that project B will succeed with probability $30\%.$ If successful, the project will generate free cash flows over the next year of $$270$ million. If it fails, free cash flows will only be $$90$ million. Both project A and project B cost $$100$ million, that the company wants to raise through debt financing.

Assume that everyone in the economy is risk neutral and the risk$-$free rate is $5\%.$ In questions $($b$)-($d$),$ assume that lenders are rational $($i$.$e$.,$ they can anticipate that the company$$s management acts in the interests of equity holders$),$ but they cannot include any protective covenants in a loan agreement.

c$)$ What interest should the company promise to pay on its debt in order to raise $$100$ million from lenders? Does the promised rate coincide with the expected rate? What is a default premium requested by lenders? $(12$ marks$)$

Therefore, the default premium $=$ promised rate $-$ expected rate $=7\mathrm{.}92\%-5\%=2\mathrm{.}92\%$