Question

Sheila Goodman recently received her MBA from the Harvard Business School. She has joined the family business, Goodman Software Products Inc., as Vice-President of Finance. She believes in adjusting projects for risk. Her father is somewhat skeptical but agrees to go along with her. Her approach is somewhat different than the risk-adjusted discount rate approach, but achieves the same objective. She suggests that the inflows for each year of a project be adjusted downward for lack of certainty and then be discounted back at a risk-free rate. The theory is that the adjustment penalty makes the inflows the equivalent of riskless inflows, and therefore a risk-free rate is justified.

A table showing the possible coefficient of variation for an inflow and the associated adjustment factor is shown next:
  

Coefficient of Variation			Adjustment Factor
0	−	.25		.90
.26	−	.50		.80
.51	−	.75		.70
.76	−	1.00		.60
1.01	−	1.25		.50

Assume a $164,000 project provides the following inflows with the associated coefficients of variation for each year.
  

Year	Inflow		Coefficient of Variation
1	$	31,700			.17
2		56,500			.25
3		75,000			.51
4		62,100			.75
5		67,800			1.07

  
Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. Fill in the table below: (Do not round intermediate calculations. Round your dollar answers to the nearest whole dollar.)
  

  
b-1. If the risk-free rate is 4 percent, compute the net present value of the adjusted inflows. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.)
  

  
b-2. Should this project be accepted?
  

	No
	Yes

Answer 1

Requirement (a) – Adjusted Inflow

Year	Adjustment Factor	Adjusted Inflow ($)
1	0.90	28,530
2	0.90	50,850
3	0.70	52,500
4	0.70	43,470
5	0.50	33,900

Requirement (b)(1) - The net present value of the adjusted inflows.

Year	Annual cash inflows ($)	Present Value factor at 4%	Present Value of Cash inflow ($)
1	28,530	0.961538	27,432.69
2	50,850	0.924556	47,013.68
3	52,500	0.888996	46,672.31
4	43,470	0.854804	37,158.34
5	33,900	0.821927	27,863.33
TOTAL			1,86,140.35

Net Present Value of the Project (NPV) = Total Present Value of Annual cash inflows - Initial Investment

= $1,86,140.35 - $164,000

= $22,140.35

Requirement (b)(2) – DECISION

“YES”. The project should be accepted, since the Net Present Value of the Project is Positive $22,140.35.

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.