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 $2,375 and the Sony will cost $2,675. 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 $410 by the end of 3 years, they expect to sell the Sony for $365 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 $895 and for the Sony to be $975. Both sets can be viewed as quality units and are equally risky purchases. They estimate their opportunity cost to be 9.4%. 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

NPV

NPV is the present value of cashflows net of the initial outlay. In the case of Samsung TV the life of asset is 3 yrs. Hence we find the present value of cash flows ( benefits derived ) from the asset from Year 0 to 3 (including salvage value at the end of 3 rd year). This is net off with the initial investment to find Net Present Value.

Similarly for Sony TV, we compute the NPV. Here the life of asset is 4 years. Hence we compute Present value of cashflows for 4 years.

ANPV

ANPV is the annualised NPV of cashflows. In case of assets with different lives, the ANPV acts as a more appropriate measure of choosing the best alternative. The NPV dividend by PV Annuity factor gives the Annualised NPV.

For Samsung TV , we use the PV annuity factor of 9.4% for 3 yrs and for Sony TV we use the PV annuity factor of 9.4% for yrs to compute ANPV of the respective assets.

2 a) NPV of Samsung HD Plasma TV 3 7 4 Year Cashflow PVIF @ 9.4% PV of CF 5 0 (2,375.00) 1.00 (2,375.00) 6 895 0.914 818.10 =B6*C6 895 0.836 747.81 895 0.764 683.55 410 0.764 313.14 10 NPV 187.59 =SUM(D5:09) 11 12 b) ANPV of Samsung HD Plasma TV براي | س | سا 9 13 14 15 16 NPV PVIFA (9.4%,3 yrs) ANPV 187.59 2.513 =SUM(C6:08) =187.59/2.513 74.64 =D14/D15 17 18

18 c) NPV of Sony HD Plasma TV 20 21 Year Cashflow PVIF @ 9.4% PV of CF 22 (2,675.00) 1.00 (2,675.00) 23 975 0.914 891.22 24 975 0.836 814.65 25 975 0.764 744.65 26 975 0.698 680.67 27 365 0.698 254.81 28 NPV 711.01 29 d) ANPV of Sony HD Plasma TV 31 32 NPV 711.01 33 PVIFA (9.4%,4 yrs) 3.211 =SUM(C23:026) 34 ANPV =711.01/3.211 35 $ 221.40

B 36 37 e) Decision 38 39 Butlers should purchase Sony HD Plasma Tv since it has higher NPV 40 and Higher Annualised NPV which implies that it gives a higher 41 benefit 12