Question

NPV and ANPV decisions   Personal Finance Problem Richard and Linda Butler decide that it is time to purchase a​ high-definition (HD) television because the technology has improved and prices have fallen over the past 3 years. From their​ research, they narrow their choices to two​ sets, the Samsung​ 64-inch plasma with 1080p capability and the Sony​ 64-inch plasma with 1080p features. The price of the Samsung is

​$2 comma 3402,340

and the Sony will cost

​$2 comma 7002,700.

They expect to keep the Samsung for 3​ years; if they buy the more expensive Sony​ unit, they will keep the Sony for 4 years. They expect sell the Samsung for

​$420

by the end of 3​ years; they expect to sell the Sony for

​$340

at the end of the year 4. Richard and Linda estimate that the​ end-of-year entertainment benefits​ (i.e., not going to movies or events and watching at​ home) from the Samsung to be

​$890

and for the Sony to be

​$1 comma 0251,025.

Both sets can be viewed as quality units and are equally risky purchases. They estimate their opportunity cost to be

8.9 %

The Butlers wish to choose the better alternative from a purely financial perspective. To perform this analysis they wish to do the​ following:

a. Determine the NPV of the Samsung HD plasma TV.

b. Determine the ANPV of the Samsung HD plasma TV.

c. Determine the NPV of the Sony HD plasma TV.

d. Determine the ANPV of the Sony HD plasma TV.

e. Which set should the Butlers purchase and​ why?

Answer 1

a). NPV of the Samsung HD plasma TV.

Year	Annual Cash Flow ($)	Present Value factor at 8.90%	Present Value of Cash Flow ($)
1	890	0.91827	817.26
2	890	0.84323	750.47
3	1,310 [890 + 420]	0.77431	1,014.35
TOTAL		2.53581	2,582.08

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

= $2,582.08 - $2,340

= $242.08

(b).Annual Net Present Value (ANPV) of the Samsung HD plasma TV.

ANPV = Net Present Value / [PVIFA 8.90%, 3 Years]

= $242.08 / 2.53581

= $95.47

(c).NPV of the Sony HD plasma TV.

Year	Annual Cash Flow ($)	Present Value factor at 8.90%	Present Value of Cash Flow ($)
1	1,025	0.91827	941.23
2	1,025	0.84323	864.31
3	1,025	0.77431	793.67
4	1,365 [1,025 + 340]	0.71103	970.56
TOTAL		3.24684	3,569.77

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

= $3,569.77 - $2,700

= $869.77

(d). Annual Net Present Value (ANPV) of the Sony HD plasma TV.

ANPV = Net Present Value / [PVIFA 8.90%, 4 Years]

= $869.77 / 3.24684

= $267.88

(e).DECISION

Richard and Linda Butler should purchase the Sony HD plasma TV, since the NPV and the ANPV is higher in Sony HD plasma TV

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.