Comparison of alternative prizes with discount rate of 6%

Question 7
A morning radio show offered the following four prizes as alternative prizes for one of its
competitions. Which prize is the most valuable if your discount rate is 6%? (Show working to
justify your answer.)
(a) $5,000 per year, forever, with the first amount paid after 1 year.
¿ t h is case , t h e winner is offered a perpetuity .
PV of a perpeuity = D
r ,
w h ere Dis t h eannual payment w h ile r is t h e discount rate
PV of t h e perpeuity= 5000
0.06 =$ 83,333.33
(b) $12,000 per year for eight years, with the first amount paid today.
PV =P ( 1+r )−n
PV =12000 ( 1.06 ) 0 +12000 ( 1.06 )−1+ ...+12000 ( 1.06 )−7
¿ 12000 (1+1.06 + 1
1.06 + 1
1.062 + 1
1.063 +...+ 1
1.067 )
¿ 12000 ( 6.58238 )=$ 78988.56
(c) $20,000 today and $80,000 six years from now.
PV =P ( 1+r )−n
PV =20000 ( 1+r )0 +80000 ( 1.06 )−6
¿ 12000+56396.84
¿ $ 76396.84
(d) $15,000 per year for ten years, with the first amount paid at year 5.
PV = ( 1+r )−n
PV = 15000
1.065 + 15000
1.066 +...+ 15000
1.069 + 15000
1.0610
¿ 15000 ( 1
1.065 +...+ 1
1.0610 )
¿ 15000∗6.247143
¿ $ 93,707.14
n
Discounting
factor ( 1.06 ) −n
5 1.06
0.74725
8
6 1.06
0.70496
1