Question

Jumbo Enterprises is evaluating an investment project with project cash flows (millions) as indicated below. The firm's cost of capital is 7.5%. What is the NPV and IRR of this project? WACC: Year Cash flows (Smillions) 7.5% 0 $350 1 $50 2 75 3 $120 4 $160 5 $190 a. NPV=$100, IRR= 16.45% b. NPV=110.16, IRR=7.5% C. NPV=110.16, IRR=16.45% d. NPV=120.5, IRR=16.45% e. NPV=5245, IRR=21.50%

Answer 1

As,

---> PV = FV / (1 + r)ⁿ

Present value of each year is calculated with help of above formula where r = 7.5 %. Cash flow of that particular year is FV and n is no. of year after which the cash flow is incurred.

For example- Present value of cash inflow for 2nd year will be calculated as under-

PV = 75 / (1 + 0.75)²

= $ 64.89994592

Likewise it is calculated for each year.

year	cashflow	present value of cash inflows
1	50	46.51162791
2	75	64.89994592
3	120	96.59526834
4	160	119.8080848
5	190	132.3461401
	total	460.1610671

NPV = Present value of cash inflows - present value of cash outflows.

Present value of cash inflows = $ 460.1610671

present value of cash outflow = $ 350

NPV = 460.1610671 - 350

= $ 110.1610671 = $110.16 (approx)

IRR of a proposal is defined as the discount rate at which NPV is 0. It is the rate at which the present value of cash inflows is equal to present value of cash outflows.

We will calculate IRR with trial and error approach.

Suppose required rate is 16 %

NPV at 16 % discount rate can be calculated as calculated above -

PV = FV / (1 + r)ⁿ

year	cashflow	present value of cash inflows
1	50	43.10344828
2	75	55.7372176
3	120	76.87892082
4	160	88.36657566
5	190	90.46147293
	Total	354.5476353

NPV = 354.5476353 - 350

= $ 4.5476353

Now NPV will be calculated with taking discount rate as 17 %

PV = FV / (1 + r)ⁿ

year	cashflow	present value of cash inflow
1	50	42.73504274
2	75	54.78851633
3	120	74.92446677
4	160	85.38400772
5	190	86.66111894
		344.4931525

NPV = 344.4931525 - 350

= $ -5.506847505

IRR = La (A-B) * * H -L

where ,

L = Lower discount rate at which NPV is positive.

H = Higher discount rate at which NPV is negative.

A = NPV at lower discount rate.

B = NPV at higher discount rate.

$IRR = 16 + \frac{4.5476353}{(4.5476353- (-5.506847505))}* (17-16)$

= 16 + 0.452299277

= 16.45 % (approx)

Hence option C is correct.

NPV = $110.16

and IRR = 16.45 %

Hope it clarifies!