Question

Mr. Graziano Pellè, the capital budgeting director of Giovinco Corporation(GC), is evaluating a five-year project, which will require an initial investment of $98,000 today. The expected end-of-year cash flows of the project are as follows: Year 1: $40,000 Year 2: $29,000 Year 3: $30,000 Year 4: $10,000 Year 5: $11,000 Weighted average cost of capital of this project is 13%, and both target payback and discounted payback is 4 years.

a. What is the IRR of this project?
b. What is the NPV of this project?
c. What is discounted payback of this project?
d. What is the payback of this project?

Answer 1

(a)Internal Rate of Return [IRR] of the Project = 9.26%

Step – 1, Firstly calculate NPV at 13%

Net Present Value [NPV] = Present Value of Annual cash flows – Initial Investment

= [$40,000 x 0.8849557] + [29,000 x 0.7831466] + [30,000 x 0.6930501] + [10,000 x 0.6133187] + [11,000 x 0.5427599] – 98,000

= [ $35,398.23 + 22,711.25 + 20,791.5 + 6,133.19 + 5,970.36 ] – 98,000

= $91,004.53 – 98,000

= - $6,995.47 [ Negative NPV]

Step – 2, NPV at 13% is Negative , Calculate the NPV again at a Lower Rate , Say 8%

NPV at 8% = $ 2,551.56 [ Positive]

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 13% + - $6,995.47 (8% - 13%)

              - $6,995.47 - 2,551.56

IRR = 13% - 3.74% = 9.26%

(b)Net Present Value [NPV] of the Project = - $6,995.47 [ Negative NPV]

Net Present Value [NPV] = Present Value of Annual cash flows – Initial Investment

Year	Cash Inflow	Present Value Factor at 13%	Present Value of cash flow
1	40,000	0.884955752	35,398.23
2	29,000	0.783146683	22,711.25
3	30,000	0.693050162	2,0791.5
4	10,000	0.613318728	6,133.19
5	11,000	0.542759936	5,970.36
			$91,004.53

Net Present Value [NPV] = Present Value of Annual cash flows – Initial Investment

= $91,004.53 – 98,000

= - $6,995.47 [ Negative NPV]

(c) Discounted payback period of the project

Year	Cash Flows	Present Value Factor at 13%	Discounted Cash flow	Cumulative Discounted cash flow
0	(98,000)	1.00000000	-98,000	-98,000
1	40,000	0.884955752	35,398.23	-62,601.77
2	29,000	0.783146683	22,711.25	-39,890.52
3	30,000	0.693050162	2,0791.5	-19,099.02
4	10,000	0.613318728	6,133.19	-12,965.83
5	11,000	0.542759936	5,970.36	-6,995.47
			$91,004.53

Average of Discounted cash flow = $91,004.53 / 5 Years = $18,200.91

Discounted Payback = Initial Investment = Average discounted cash flow

= $98,000 / 18,200.91

= 5.384 Years

With the given discount rate of 13%, the Investment project will not payback within the first 5 years.

Average discounted payback is 5.384 years [ $98,000 /18,200.91 ]

(d) Payback Period of the Project = 2.967 Years

Year	Cash Flows	Cumulative net Cash flow
0	(98,000)	(98,000)
1	40,000	(58,000)
2	29,000	(29,000)
3	30,000	1,000
4	10,000	11,000
5	11,000	22,000
	Payback Period =	2.967 Years

Payback Period=Years before full recover + (Unrecovered cash inflow at start of the year/cash flow during the year )

= 2 Year + ( 29,000 / 30,000 )

= 2 Year + 0.967 Year

= 2.967 Years