Question

Question.	Your boss has instructed you to evaluate a new project the firm has been considering moving forward with. Other analysts in the firm have identified projected cash flows for the project, which are shown below. The firm's WACC is 9.7%. Given the additional risk of this project, your boss has asked you to add 1.2% to the discount rate for this project. Identify the project's Net Present Value, Internal Rate of Return, and Discounted Payback Period (with fractional years calculated).
		Year	0	1	2	3	4	5
		Cash Flow	-27,500	-3,000	$8,000	$11,800	$14,500	$11,000
	Net Present Value
	Internal Rate of Return
	Discounted Payback Period

Answer 1

Net Present Value (NPV)

Year	Annual Cash Flow ($)	Present Value factor at 9.70%	Present Value of Cash Flow ($)
1	-3,000.00	0.91158	-2,734.73
2	8,000.00	0.83097	6,647.78
3	11,800.00	0.75750	8,938.45
4	14,500.00	0.69052	10,012.48
5	11,000.00	0.62946	6,924.04
TOTAL			29,788.01

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

= $29,788.01 - $27,500

= $2,288.01

“The Net Present Value = $2,288.01”

Internal Rate of Return (IRR)

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 12%

Year	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	-3,000.00	0.89286	-2,678.57
2	8,000.00	0.79719	6,377.55
3	11,800.00	0.71178	8,399.01
4	14,500.00	0.63552	9,215.01
5	11,000.00	0.56743	6,241.70
TOTAL			27,554.69

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

= $27,554.69 – 27,500

= $54.69

Step – 2, NPV at 12% is positive, Calculate the NPV again at a higher discount rate, Say 13%

Year	Annual Cash Flow ($)	Present Value factor at 13%	Present Value of Cash Flow ($)
1	-3,000.00	0.88496	-2,654.87
2	8,000.00	0.78315	6,265.17
3	11,800.00	0.69305	8,177.99
4	14,500.00	0.61332	8,893.12
5	11,000.00	0.54276	5,970.36
TOTAL			26,651.78

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

= $26,651.78 - 27,500

= -$848.22 (Negative)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.12 + [$54.69 x (0.13 – 0.12)]

              $54.69 – (-$848.22)

= 0.12 + 0.0006

= 0.1206

= 12.06%

“The Internal Rate of Return (IRR) = 12.06%”

Discounted Payback Period

Year	Cash Flows	Present Value Factor at 9.70%	Discounted Cash Flow	Cumulative net discounted Cash flow
0	-27,500.00	1.00000	-27,500.00	-27,500.00
1	-3,000.00	0.91158	-2,734.73	-30,234.73
2	8,000.00	0.83097	6,647.78	-23,586.95
3	11,800.00	0.75750	8,938.45	-14,648.50
4	14,500.00	0.69052	10,012.48	-4,636.03
5	11,000.00	0.62946	6,924.04	2,288.01

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

= 4 Year + ($4,636.03 / $6,924.04)

= 4 Year + 0.67 Years

= 4.67 Years

“The Discounted Payback Period = 4.67 Years”

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.