Question

Assume it costs $11,000 for a new pizza oven. You expect the new pizza oven to provide $2,000 each year in net income for 8 years. Should you invest in the pizza oven if you have a required rate of return of 12%.

-Does it seem likely the pizza oven would only last 8 years?

-What if it lasts 15 years?

Answer 1

Let’s compute NPV for the investment.

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 12 % (F)	PV (= C x F)
0	($11,000)	1/(1+0.12)^0	1	($11,000.0000)
1	$2,000	1/(1+0.12)^1	0.8928571428571	$1,785.7143
2	$2,000	1/(1+0.12)^2	0.7971938775510	$1,594.3878
3	$2,000	1/(1+0.12)^3	0.7117802478134	$1,423.5605
4	$2,000	1/(1+0.12)^4	0.6355180784048	$1,271.0362
5	$2,000	1/(1+0.12)^5	0.5674268557186	$1,134.8537
6	$2,000	1/(1+0.12)^6	0.5066311211773	$1,013.2622
7	$2,000	1/(1+0.12)^7	0.4523492153369	$904.6984
8	$2,000	1/(1+0.12)^8	0.4038832279794	$807.7665
			NPV	($1,064.7205)

NPV is - $ 1,064.72. There is a loss on investment as NPV is negative and hence investment is not recommended.

The oven may last more or less than 8 years depending upon its performance.

Let’s compute NPV if it runs for 15 years.

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 12 % (F)	PV (= C x F)
0	($11,000)	1/(1+0.12)^0	1	($11,000.0000)
1	$2,000	1/(1+0.12)^1	0.8928571428571	$1,785.7143
2	$2,000	1/(1+0.12)^2	0.7971938775510	$1,594.3878
3	$2,000	1/(1+0.12)^3	0.7117802478134	$1,423.5605
4	$2,000	1/(1+0.12)^4	0.6355180784048	$1,271.0362
5	$2,000	1/(1+0.12)^5	0.5674268557186	$1,134.8537
6	$2,000	1/(1+0.12)^6	0.5066311211773	$1,013.2622
7	$2,000	1/(1+0.12)^7	0.4523492153369	$904.6984
8	$2,000	1/(1+0.12)^8	0.4038832279794	$807.7665
9	$2,000	1/(1+0.12)^9	0.3606100249816	$721.2200
10	$2,000	1/(1+0.12)^10	0.3219732365907	$643.9465
11	$2,000	1/(1+0.12)^11	0.2874761040988	$574.9522
12	$2,000	1/(1+0.12)^12	0.2566750929454	$513.3502
13	$2,000	1/(1+0.12)^13	0.2291741901298	$458.3484
14	$2,000	1/(1+0.12)^14	0.2046198126159	$409.2396
15	$2,000	1/(1+0.12)^15	0.1826962612642	$365.3925
			NPV	$2,621.7290

NPV of the oven for 15 years life at 12 % interest rate is $ 2,621.73

As NPV is positive, investment is profitable and recommended.