Question

Year Cash Flow Ins 1 $20,000 2 $40,000 3 $40,000 4 $20,000 5 $30,000 Rieger International is attempting to evaluate the feasibility of investing $96000 in a piece of equipment that has a 5 -year life. The firm has estimated the cash inflows associated with the proposal as shown in the following table. The firm has a 9 % cost of capital. a. Calculate the payback period for the proposed investment. b. Calculate the net present value (NPV) for the proposed investment. c. Calculate the internal rate of return (IRR), rounded to the nearest whole percent, for the proposed investment. d. Evaluate the acceptability of the proposed investment using NPV and IRR. What recommendation would you make relative to implementation of the project?

Answer 1

(a)-Payback Period for the Project

Year	Cash Flows ($)	Cumulative net Cash flow ($)
0	-96,000	-96,000
1	20,000	-76,000
2	40,000	-36,000
3	40,000	4,000
4	20,000	24,000
5	30,000	54,000

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

= 2 Year + ($36,000 / $40,000)

= 2 Year + 0.90 Years

= 2.90 Years

(b)-Net Present Value (NPV)

Year	Annual Cash Inflow ($)	Present Value Factor at 9%	Present Value of Annual Cash Inflow ($)
1	20,000	0.91743	18,348.62
2	40,000	0.84168	33,667.20
3	40,000	0.77218	30,887.34
4	20,000	0.70843	14,168.50
5	30,000	0.64993	19,497.94
TOTAL			1,16,569.61

Net Present Value = Present Value of annual cash inflows – Present value of cash outflows

= $1,16,569.61 - $96,000

= $20,569.61

NOTE

The Formula for calculating the Present Value Factor is is [1/(1 + r)ⁿ], Where “r” is the Discount Rate and “n” is the number of years.

(c)-Internal Rate of Return (IRR)

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 16%

Year	Annual Cash Flow	Present Value factor at 16%	Present Value of Cash Flow
1	20,000	0.86207	17,241.38
2	40,000	0.74316	29,726.52
3	40,000	0.64066	25,626.31
4	20,000	0.55229	11,045.82
5	30,000	0.47611	14,283.39
TOTAL			97,923.41

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $97,923.41 - $96,000

= $1,923.41

Step – 2, NPV at 16% is positive, Calculate the NPV again at a higher discount rate, Say 18%

Year	Annual Cash Flow	Present Value factor at 18%	Present Value of Cash Flow
1	20,000	0.84746	16,949.15
2	40,000	0.71818	28,727.38
3	40,000	0.60863	24,345.23
4	20,000	0.51579	10,315.78
5	30,000	0.43711	13,113.28
TOTAL			93,450.82

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $93,450.82 - $96,000

= -$2,549.18 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.16 + [$1,923.41 x (0.18 – 0.16)]

              $1,923.41 – (-$2,549.18)

= 0.16 + 0.0084

= 0.1684

= 16.84%

“Therefore, The Internal Rate of Return (IRR) for the Project = 16.84%”

(d)-DECISION

Rieger International should “ACCEPT” the Proposed Investment Project, Since the NPV of the Project is Positive $20,569.61 and the IRR (16.84%) is greater than the Cost of Capital of 9%, and therefore, the project should be accepted.