Question

Elinor is asked to invest $5100 in a friend's business with the promise that the friend will repay $5610 in one year. Eleanor finds her best alternative to this investment, with similar risk, is one that will pay her $5508 in one year. U.S. securities of similar term offer a rate of return of 7%. What is the opportunity cost of capital in this case

Answer 1

Answer:

the opportunity cost of capital in this case is 8%

Explanation:

From the information given :

Elinor is asked to invest $5100 in a friend's business with the promise that the friend will repay $5610 in one year.

Eleanor finds her best alternative to this investment, with similar risk, is one that will pay her $5508 in one year.

U.S. securities of similar term offer a rate of return of 7%.

The opportunity cost of capital can be determined by using the expression:

$A = P ( \dfrac{1+r}{100})^n$

where;

A = amount = $5508

P = Principal = $5100

r = opportunity cost of capital  = ???

n = number of years = 1 year

$5508= 5100 ( {1+ \dfrac{r}{100})^1$

$\dfrac{5508}{5100}= ( {1+ \dfrac{r}{100})^1$

$1.08 = ( {1+ \dfrac{r}{100})$

$1.08 = \dfrac{100 + r}{100}$

1.08 × 100 = 100 + r

108 = 100 + r

r = 108 - 100

r = 8%

Therefore; the opportunity cost of capital in this case is 8%