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 ​$2,320 and the Sony will cost ​$2,735. 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 $330 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 ​$945 and for the Sony to be ​$985. Both sets can be viewed as quality units and are equally risky purchases. They estimate their opportunity cost to be 8.8 %. 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 = Total pv of inflows -Initial outflow Discount rate = 8.8%

ANPV=NPV/Pressent Value of Annuity Factor

a)Samsung HD plasma Tv Initial outflow = $2320 Benefits of $945 for 3 years and sold at end of year 3 so Final year benefit of $945+$420=$1365.Total PV of inflows = $945*.919=$868.45+$945*.844=$797.58 Year 3 = $1365*.7764=$1059.786 Total = $2725.81 NPV =$2725.81-$2320=$405.81

b)ANPV=NPV/PVAF

PVAF PVAF =1-(1+r)^(-n)of 3years at 8.8 =2.540 NPV= $405.81 ANPV=$405/2.540=$159.448

c)Sony HD TV Initial Outflow=$2735 Benefits(inflow) of $985 p.a for 4 years . At the end of year 4 its sold for $330 So the YEar 4 cashflow =$330+$985=$1315.Total PV of inflows = $985*.919=$905.215 Year 2 = $985*.844=$$831.34 Year 3 =$985*.7764=$764.75 Year $ =$1315*.7136=$938.384 Total =$3439.689 NPV=$3439.689-$2735=$704.689

d)ANPV =NPV/PVAF

PVAF PVAF =1-(1+r)^(-n) for 4 years at 8.8% =3.254 NPV =$704.689 ANPV = $704.689/3.254=$216.56

e)The Butlers should purchase the Sony HD plasma Tv due to its higher ANPV.ANPV converts NPV into its annual annuity value and thereby is the most efficient method while selecting mutually exclusive investments of unequal lives.