Question

5.         I’ve spent $10,000 to install high efficiency windows in my home. They are expected to last 20 years.   I expect my annual heating bill to decrease by $1,000.

a.         What is the “net present value of my investment? Use a discount rate that is appropriate for YOU as an individual?  

b.         If city hall had made this investment, what is the “payback” time? Use a discount rate appropriate for a public project.

c.         Calculate the “Internal Rate of Return” for this project. Would a profit maximizing company be willing to invest in this project at their corporate offices?

Answer 1

We will use a discount rate of 6%

a) We will calculate the present value of 1000 saving annually for 20 years

PV = 1000 * PVAF 6%, 20

PV = 1000 * 11.4699 = 11469.9

NPV = 11469 - 10000 = 1469

Calculation of Discounted Payback

Year	Saving	PV Factor @ 6%	PV	Cumulative
1	1000	0.94	943.40	943.40
2	1000	0.89	890.00	1,833.39
3	1000	0.84	839.62	2,673.01
4	1000	0.79	792.09	3,465.11
5	1000	0.75	747.26	4,212.36
6	1000	0.70	704.96	4,917.32
7	1000	0.67	665.06	5,582.38
8	1000	0.63	627.41	6,209.79
9	1000	0.59	591.90	6,801.69
10	1000	0.56	558.39	7,360.09
11	1000	0.53	526.79	7,886.87
12	1000	0.50	496.97	8,383.84
13	1000	0.47	468.84	8,852.68
14	1000	0.44	442.30	9,294.98
15	1000	0.42	417.27	9,712.25
16	1000	0.39	393.65	10,105.90
17	1000	0.37	371.36	10,477.26
18	1000	0.35	350.34	10,827.60
19	1000	0.33	330.51	11,158.12
20	1000	0.31	311.80	11,469.92

Payback = 15 + (10000-9712.25)/393.65

Payback = 15 + 0.73 Years

Payback = 15.73 Years

c) Use the following table to calculate IRR

Year	Saving
0	-10000
1	1000
2	1000
3	1000
4	1000
5	1000
6	1000
7	1000
8	1000
9	1000
10	1000
11	1000
12	1000
13	1000
14	1000
15	1000
16	1000
17	1000
18	1000
19	1000
20	1000

Use =IRR in excel and select cash flow from Year 0-20

IRR = 7.75%

To accept a project IRR should be more than required rate of return

Since 7.75% IRR is more than required rate of return of 6%

conmapny should invest in the project