Question

Assume you have two investment options, Option A, which earns 3.5% and starts with a payment of $18,000 in Year 1 (age 41), and Option B, which earns 6.0% and has a first payment of $25,000 but doesn’t start paying until Year 6. The opportunity cost is 8.0%. What is the NPV of Option A through 20 years?

a. What is the NPV of Option B through 20 years?

b. In what year (not age) does Option A first pay more than $25,000? (list the number only (e.g., “16” but do not include the parentheses).

c. What is the difference in income payment between Option A and Option B in Year 18? (list as negative (e.g., - $10,000) if Option B – Option A = negative; list as positive (e.g., $10,000) if Option B – Option A = positive).

d. What is the IRR in year 13 for choosing Option B instead of Option A?

e. What year does the IRR turn positive if choosing Option B? (list the number only).

f. What is the NPV of Option B through 20 years if it starts paying the $25,000 at Year 5 instead of Year 6?

g. Now what year (not age) does the IRR turn positive if choosing Option B? (list the number only).

Answer 1

B C D E F G H I J K L 10 M N O P Q R S T U V 20 W X Y Z AA AB AC ADI 0 1 2 3 4 5 6 7 8 9 11 12 13 14 15 16 17 18 19 4 A 1 Year 2 Option A 3 payment 4 NPY 19282 19957 2065521378 22127 22901 23703 24532 25391 26279 27199 28151 29137 30156 31212 32304 33435 18000 18630 $229,237.75 =NPV(8%B3:03) 34605 Each year payment increases by 3.5% as compared to prior year 6 Option B 7 payment 8 NPY 25000 26500 28090 2977531562 33456 35463 37591 39846 42237 44771 47457 50305 53323 56523 Each year payment increases by 6% as compared to prior year $208,007.42 ENPV[8%,G7:07)/1.085 11 12 b) C) In year 11, option A pays 25390.8 In year 18, option payment Option A payment = Option B payment = Option B - Option A = 14 32304.16 50304.91 18000.752 15 d) 17 18 Choosing Option B over Option A Effective cash floy - 18000 18630 -19282 IRR for year 13 -7.68% - IRR(C18:018,6%) - 19957 -20655 3621.6 4373.4 5189 6072.8 7029.8 8064. 9 9183.5 10392 11695 13100 14615 16246 18001 19888 21918 20 21 e) 22f) 1.2946% =IRR(C18:S18,6%) IRR will positive in year 17, with IRR of If option payment starts in year 5 Cash flows will be 25000 26500 28090 29775 31562 33456 35463 37591 39846 42237 44771 47457 50305 53323 56523 59914 25 Payment 26 NPY $237,502.44 =NPV(8%,G25:V25)/1.0894 28 9) Same as question E