Question

A firm wants to undertake an investment project which costs N$25,000, which it wants to finance through a bank loan. The project has a 60 percent probability of success. If the project succeeds the firm will make a cash flow of N$75,000 after a year. If it fails the firm will get a cash flow of N$10,000 and will be required to pay the whole amount to the bank. The bank has a required return of 25%.

(a) What will be the bank’s loan rate at which it will be willing to lend? Explain.

(b) How much will be the bank’s safe income? (1 mark)

(c) How is the bank’s lending rate related to the probability of failure? Explain your answer.

(d) What will be the firm’s expected profit at the rate in (a)? Will the firm be willing to participate at that rate?

(e) How much will be the bank’s uncertain income? What will be the expected values of these incomes?

Answer 1

(a). Bank's loan rate at it will wiiling to lend

Bank required rate of return is 25%.(It is given in question).

Therefore, Bank will be willing to lend @ 25%. p.a.

Further, the firm has to repay the loan to bank along with the interest amount , irrespective of the fact that the project suceeds or fail.

(b) Bank's safe Income

Bank's Safe Income will be N$10,000. Because even if the projects fails , firm will get cash flow of Rs. 10,000.

(c) How bank's lending rate relatable to the probability of failure

Due to credit risk ; banks need to check the probability of failure of the project and according need to decide the lending rate.

Credit Risk is a risk of default may be made by the borrower in the principal and interest amount .

(d) Firm's expected profit at the rate calculated in (a).

If the project succeds :

Cash Inflow after 1 year : N$75,000

Less : Cash outflow : N$25,000

Less : Interset amount : N$2,851

Expected profit : N$47,149

If the project fails :

Cash Inflow after 1 year : N$10,000

Cash outflow : N$25,000

Less : Interset amount : N$2,851

Expected profit : N$(17,851)

In the case project succeds , the firm will be able to repay its loan along with Interest amount, Thus the firm will be willing to perticipate at that rate.

(e) Bank's uncertain Income :

IN case the project goes successful ; bank will get the entire amount of N$ 27,851 (Principal and interest). So, there is no uncertain Income in this case.

Further, where the projects gets fail , bank will not be able to recover N$ 17,851 (out of cash inflow of N$ 10,000), so in this case uncertain Income to bank will be N$ 17,851.(only fetch N$ 10,000 from the firm).

Expected value of these Income =

1. N$ 27,581*0.60 = N$ 16,548.60

2. N$ 10,000 * 0.40 = N$ 4,000

= N$ 20,548.60