You are considering investing in a start up project at a cost of $100,000. You expect the project to return $500,000 to you in seven years. Given the risk of this project, your cost of capital is 20% p. a. compounded annually. The IRR for this project is closest to:a 20.00%b 25.85%c 15.60%d 18.95%

b.The IRR is equal to 25.85%

Explanation:

Firstly we are given that i consider investing $100000 which will in this problem be our Cinitial which is the initial investment for the project.

Then now given the risk of this project, my cost of capital is 20% so then we will compare this to the IRR and see if i can accept the project or not if the cost of capital is greater than the IRR than its not good to invest on the project but if the cost of capital is less than the IRR then the this will be a good investment as the cost of capital also checks the opportunity cost.

The future payment cash flows which is $500000 so we will use the following formula:

NPV = (cash flow)/(1+IRR)^n     - initial investment

so we find the present value of the cash flow of the investment and subract the initial investment which will give us a zero cause the present value of the cash flow is equal to the initial investment therefore( n is the period of cash flows):

0= $500000/(1+IRR)^7    - $100000 transpose the initial investment and solve for IRR.

$100000(1+IRR)^7= $500000 then divide both sides by $100000

(1+IRR)^7 =  5          then find the 7nth root of both sides to eliminate the exponent of 7

1+ IRR =

1+IRR = 1.258498951 then subtract 1 both sides to solve for IRR

IRR = 0.258498... then multiply by 100 as IRR is a percentage

IRR= 25.85 % rounded off to two decimal places which is the answer b

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