Assignment 7

Answer:

14.1
Solution: Inflated dollars are converted into constant-value dollars by dividing by one plus the
inflation rate per period for however many periods are involved – Explain a bit more
14.2
Solution: Cost will double in 10 years when the value of the money has decreased by exactly one
half. From Eq. [14.3]
1(1 + f)10 = 2
(1 + f) = 2 0.1
= 1.0718
f = 0.0718 (7.18% per year)

14.8
Solution: a) Freshman year cost = 19,548(1.07)3 = $23,947

(b) Second year cost = (19,548 + 4000)(1.07)4 = $30,867

Explain in detail above calculations

14.4
Solution: 14.14 23,930,909 = 1,000,000(1 + f)103
(1 + f)103 = 23.9309
1 + f = (23.9309)0.00971

f = 0.0313 (3.13% per year)

14.26
Solution: (a) Use if for future dollars and i for CV dollars
if = 0.10 + 0.06 + (0.10)(0.06) = 0.166 (16.6%)
PW = 16,000 + 40,000(P/F,16.6%,3) + 12,000(P/F,16.6%,4) + 26,000(P/F,10%,7)
= 16,000 + 40,000(0.63082) + 12,000(0.54101) + 26,000(0.51316)
= $61,067
(b) Convert CF in year 7 to future dollars and develop NPV function

14.28
Solution: 14.28 (a) Use real i = 10%
PW = 81,000(P/F,10%,2)
= 81,000(0.8264)
= $ 66,938 < $68,000 Purchase later for $81,000 b) Use if = 0.10 + 0.05 + (0.10)(0.05) = 0.155 (15.5% per year) PW = 81,000(P/F,15.5%,2) = 81,000[1/(1 + 0.155)2] = 81,000(0.7496) = $60,719 < $68,000 Purchase later for $81,000 14.39 Solution: 14.39 (a) F = 10,000(F/P,10%,5) = 10,000(1.6105) = $16,105 (b) Purchasing power = 16,105/(1 + 0.05)5 = $12,619 (c) if = i + 0.05 + (i)(0.05) 0.10 = i + 0.05 + (i)(0.05) 1.05i = 0.05 i = 0.0476 (4.76%) or use Equation [14.9] i = (0.10 – 0.05)/(1 + 0.05) = 0.0476 (4.76%) 18.2 Solution : (a) By hand: Invest now: FW = -80,000(F/P,20%,5) + 26,000(F/A,20%,5) = -80,000(2.4883) + 26,000(7.4416) = $-5582 (< 20% per year) Invest 1 year from now: FW = -80,000(F/P,20%,4) + 31,000(F/A,20%,4) = -80,000(2.0736) + 31,000(5.3680) = $520 (> 20% per year)
Invest 2 years from now: FW = -80,000(F/P,20%,3) + 37,000(F/A,20%,3)
= -80,000(1.7280) + 37,000(3.6400)
= $-3560 (< 20% per year) Timing will affect the return requirement of 20%; invest 1 year from now. (b) Spreadsheet: Same result using the FV function = - FV(20%,n,savings,-80000) 18.19 Solution: Plan 1 - Lease Opt: $0.40 per ton (AOC = $2000) AW = -60,000(A/P,12%,5) - 0.40(100)(50) = -60,000(0.27741) - 2000 = $-18,645 ML: $0.50 per ton (AOC = $2500) AW = -60,000(A/P,12%,5) - 0.50(100)(50) = -60,000(0.27741) - 2,500 = $-19,145 Pess: $0.95 per ton (AOC = $3750) AW = -60,000(A/P,12%,5) – 0.95(100)(50) = -60,000(0.27741) – 3750 = $-21,395 Plan 2 – Rental AW = -15,000 - 50(8)(15.00) = $-21,000 per year Plan 1 (lease -- optimistic and most likely) are better than rental. However, the leasepessimistic AW ($-21,395) is slightly higher than the rental option ($-21,000). 18.30 Solution: E(Income) = 1/12[500,000(4) + 600,000(2)+ 700,000(1) + 800,000(2) + 900,000(3)] = 8,200,000/12 = $683,333 19.1 Solution: (a) Discrete (b) Discrete (c) Continuous (d) Continuous (e) Discrete 19.2 Solution: (a) Continuous (assumed) and uncertain (b) Discrete with risk (c) Two variables: first is discrete and certain at $800; second is continuous for ≥ $800, but uncertain (at this point) (d) Discrete with risk (e) Discrete and certain