Question

 Rieger International is evaluating the feasibility of investing $94,000 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:

1   $20,000
2   $25,000
3   $40,000
4   $40,000
5   $25,000

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?

Show all work

Answer 1

(a)-Payback Period

Year	Cash Flows	Cumulative net Cash flow
0	-94,000	-94,000
1	20,000	-74,000
2	25,000	-49,000
3	40,000	-9,000
4	40,000	31,000
5	25,000	56,000

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

= 3 Year + ($9,000 / $40,000)

= 3 Year + 0.23 years

= 3.23 Years

(b)-Net Present Value (NPV)

Year	Annual Cash Flow ($)	Present Value factor at 9%	Present Value of Cash Flow ($)
1	20,000	0.91743	18,348.62
2	25,000	0.84168	21,042.00
3	40,000	0.77218	30,887.34
4	40,000	0.70843	28,337.01
5	25,000	0.64993	16,248.28
TOTAL			1,14,863.26

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

= $1,14,863.26 - $94,000

= $20,863.26

(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	25,000	0.74316	18,579.07
3	40,000	0.64066	25,626.31
4	40,000	0.55229	22,091.64
5	25,000	0.47611	11,902.83
TOTAL			95,441.23

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

= $95,441.23 - $94,000

= $1,441.23

Step – 2, NPV at 16% is positive, Calculate the NPV again at a higher discount rate, Say 17%

Year	Annual Cash Flow ($)	Present Value factor at 17%	Present Value of Cash Flow ($)
1	20,000	0.85470	17,094.02
2	25,000	0.73051	18,262.84
3	40,000	0.62437	24,974.82
4	40,000	0.53365	21,346.00
5	25,000	0.45611	11,402.78
TOTAL			93,080.46

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

= $93,080.46 - $94,000

= -$919.54 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.16 + [$1,441.23 x (0.17 – 0.06)]

              $1,441.23 – (-$919.54)

= 0.16 + 0.0061

= 0.1661

= 16.61%

“Therefore, the Internal Rate of Return (IRR) = 16.61%”

(d)-DECISION

Rieger International should accept the project, since the Net Present Value of the Proposed Investment is Positive $20,863.26 and the Internal Rate of Return (16.61%) is greater than the cost of capital (9%) of the proposed investment.

NOTE

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