Question

A young software genius is selling the rights to a new video game he has developed. Two companies have offered him contracts. The first contract offers 11,000 at the end of each year for the next five years, and then 18,500 dollars per year for the following 10 years. The second offers 10 payments, starting with 12,000 at the end of the first year, 15,000 dollars at the end of the second year, and sof forth, increasing by G dollars each year (i.e., the tenth payment will be (12,000 dollars + 9 x G dollars). Assume the genius uses a MARR of 11%. Which contract should the young genius choose? Use a present worth comparison and least common multiple of repeated lives {Perform all calculations using 5 significant figures and round any monetary answers to the nearest cent}.

For one life of project one, the present worth is: ?

For repeated lives of project one, the present worth is?

For one life of project two the present worth is?

For repeated lives of project two, the present worth is?

Which project is the better one?

Answer 1

Analysis period will be 30 years which is the LCM of 15 & 10 years.

MARR = 11%

(I) NPW for one life cycle for project 1:
= 11000 * (P/A, 11%,5) + 18500 * (P/A, 11%,10) * (P/F, 11%,5)
= 11000*(3.69590) + 18500*(5.88923)*(0.59345)
= 40654.90+64656.83
= $105311.73

(II) NPW for repeated life cycle for project 1:
= 105311.73 + 105311.73*(P/F, 11%,15)
= 105311.73 + 105311.73*0.20900
= 105311.73+22010.15
= $127321.88

(III) NPW for one life cycle for project 2:
G = 15000 - 12000 = 3000
= 12000 * (P/A, 11%,10) + 3000 * (P/G, 11%,10)
= 12000*(5.88923) + 3000*(21.522)
= 70670.76+64566
= $135236.76

(IV) NPW for repeated life cycle for project 2:
= 135236.76+ 135236.76 * (P/F, 11%,10) + 135236.76 * (P/F, 11%,20)
= 135236.76 + 135236.76*(0.35218) + 135236.76*(0.12403)
= 135236.76+47627.68+16773.42
= $199637.86

(V) As the NPW for for repeated life cycle for project 2 is more, project 2 should be chosen.