Question

Exercise 17.9

The state of Glottamora has $200 million remaining in its budget for the current year. One alternative is to give Glottamorans a one-time tax rebate. Alternatively, two proposals have been made for state expenditures of these funds. The first proposed project is to invest in a new power plant, costing $200 million and having an expected useful life of 20 years. Projected benefits of the new power plant are as follows:

Years	Benefits per Year
	($ Millions)
1 - 5	0
6 - 20	40

The second alternative is to undertake a job retraining program, also costing $100 million and generating the following benefits:

Years	Benefits per Year
	($ Millions)
1 - 5	40
6 - 10	28
11 - 20	8

The state Power Department argues that a 5 percent discount factor should be used in evaluating the projects because that is the government’s borrowing rate. The Human Resources Department suggests using a 12 percent rate because that more nearly equals society’s true opportunity rate. The present value interest factor at the end of years from 0 - 20 for the two discount rates are given in the following table.

Discount Rates	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
5%	1.000	0.952	0.907	0.864	0.823	0.784	0.746	0.711	0.677	0.645	0.614	0.585	0.557	0.530	0.505	0.481	0.458	0.436	0.416	0.396	0.377
12%	1.000	0.893	0.797	0.712	0.636	0.567	0.507	0.452	0.404	0.361	0.322	0.287	0.257	0.229	0.205	0.183	0.163	0.146	0.130	0.116	0.104

Evaluate the projects using both the 5 percent and the 12 percent rates.

Project	Net Benefits at Discount Rate = 5%	Net Benefits at Discount Rate = 12%
	($ Millions)	($ Millions)
Power Plant
Job Retraining Program

If you agree with the Power Department that the government’s borrowing rate is the appropriate discount rate, which project will you choose?

Job retraining program

Power plant

Answer 1

Cost of power plant = 200m

Cost of training program = 100m (Note here cost of training program is given as 100m not 200m in the question)

when i=5%

Present value of benefits from power plant = 40m *(P/A, 5%,15)* (P/F,5%,5)

= 40m *10.37965804* 0.78352616 = 325,309,344.20

Net present value of Power plant = Present value of benefits - cost

= 325,309,344.20 - 200,000,000 = 125,309,344.2

Present value of benefits from training program = 40m*(P/A, 5%,5) + 28m*(P/A, 5%,5)*(P/F,5%,5) + 8m*(P/A, 5%,10)*(P/F, 5%,10)

= 40m*4.32947667 + 28m*4.32947667*0.78352616 + 8m*7.72173492*0.61391325

= 306,086,104.3

Net present value of benefits from training program = Present value of benefits - cost

= 306,086,104.3 - 100000000 = 206,086,104.3

when i=12%

Present value of benefits from power plant = 40m *(P/A, 12%,15)* (P/F,12%,5)

= 40m *6.81086448* 0.56742685 = 154,586,695.10

Net present value of Power plant = Present value of benefits - cost

= 154,586,695.10 - 200,000,000 = -45,413,304.9

Present value of benefits from training program = 40m*(P/A,12%,5) + 28m*(P/A, 12%,5)*(P/F,12%,5) + 8m*(P/A, 12%,10)*(P/F, 12%,10)

= 40m*3.604776202 + 28m*3.604776202*0.56742685 + 8m*5.65022302*0.32197323

= 216,017,323.10

Net present value of benefits from training program = Present value of benefits - cost

= 216,017,323.10 - 100000000 = 116,017,323.10

When we choose i=5%, then Job training program would be selected as it has higher NPV

(If Job training would be costing 200m then Power Plant would have been selected, Because then NPV of Power Plant would have been high)