Question

Tipton Industries is considering a project that has the following cash flows:

Year Cash Flow

0 -6,500

1 2,000

2 3,000

3 3,000

4 1,500

The project has a WACC (cost of capital) of 12%

a. what is the firm's payback?

b. what is the NPV?

c. what is the IRR?

d. is this profit profitable? explain

Answer 1

cost of capital, WACC, (R)= 12% = 0.12

Cash flow for year 1, C1 = $2000

Cash flow for year 2, C2 = $3000

Cash flow for year 3, C3 = $3000

Cash flow for year 4, C4 = $1500

Initial investment , I = $6500

a)

payback period = period it takes for the cash flows of the project to recover the initial investment of project

we can see that in 2 years , the sum of cash flows = 2000 + 3000 = 5000

and sum of cash flows in 3 years = 5000 + 3000 = 8000

hence the payback period is in between 2 and 3 year

cash flow remaining to be recovered after 2 years = initial investment - cash flow recovered in 2 years = 6500 - 5000 = $1500

payback period = 2 + ( cash flow remaining to be recovered after 2 years)/(total cash flow in 3rd year)

= 2 + (1500)/(3000) = 2.5 years  

b) NPV = [ (C1/(1.12)¹) + (C2/(1.12)²) + (C3/(1.12)³) + (C4/(1.12)⁴) ] - I

=  [ (2000/(1.12)¹) + (3000/(1.12)²) + (3000/(1.12)³) + (1500/(1.12)⁴) ] - 6500

= [1785.71429 + 2391.58163 + 2135.34074 + 953.27712 ] -6500 = $765.9138 or $765.91

c)

IRR is the rate of return for which NPV = 0

NPV = Present value of cash inflows of the project - initial investment

Putting NPV = 0

Present value of cash inflows of the project = initial investment

[ (C1/(1+IRR)¹) + (C2/(1+IRR)²) + (C3/(1+IRR)³) + (C4/(1+IRR)⁴) ] = I

[ (2000/(1+IRR)¹) + (3000/(1+IRR)²) + (3000/(1+IRR)³) + (1500/(1+IRR)⁴) ] = 6500

We have to find IRR by trial and error method

by assuming any value and substituting the assumed value in the above equation

we want IRR such that

Left Hand side of equation(LHS) = Right hand side of equation (RHS) = 6500

by following this method we find that for IRR = 17.59014% or 17.59%

d) This project is profitable since its NPV is positive and Its IRR > WACC

which means that the project adds value to the firm