# Spoiler: CFAI 2007 Morning Q1

In part (a), the answer says the return objective calculated as follow: ----- Before inflation: N=35, pv = 4 million, pmt = –205,000, fv = –3 million, compute i/y = 4.84% inflation adjusted return: = 4.84 + 2.5% = 7.34% (or by compounding) ---- My question is in the calculation of pre-inflation return, I guess all number should be in term of today’s dollar. So I wonder pmt should be -200,000, not -205,000, even it is paid one year later. (Note fv is in term of today’ dollar. The nominal required fv is 3m*(1.025%)^35)

the Q said they are withdrawing the 200,000 immediately…

I sort of verifying it with excel, pmt should be 200,000 instead of 205000 ------------------------------------------------------------------------------------------------------ required return before inflation: N=35, pv = 4 million, pmt = –200,000, fv = 3 million, compute i/y = 4.705898% inflation adjusted return = (1+4.705898%)*(1+2.5%)=1.07323546 time starting value ending value withdraw after withdraw real income ---- ----------------- ---------------- --------------- ------------------ --------------- 00 4,000,000.00 4,292,941.84 205,000.00 4,087,941.84 200,000.00 01 4,087,941.84 4,387,324.14 210,125.00 4,177,199.14 200,000.00 02 4,177,199.14 4,483,118.24 215,378.13 4,267,740.12 200,000.00 03 4,267,740.12 4,580,290.03 220,762.58 4,359,527.45 200,000.00 04 4,359,527.45 4,678,799.45 226,281.64 4,452,517.80 200,000.00 05 4,452,517.80 4,778,599.99 231,938.68 4,546,661.31 200,000.00 06 4,546,661.31 4,879,638.14 237,737.15 4,641,900.99 200,000.00 07 4,641,900.99 4,981,852.75 243,680.58 4,738,172.17 200,000.00 08 4,738,172.17 5,085,174.39 249,772.59 4,835,401.79 200,000.00 09 4,835,401.79 5,189,524.67 256,016.91 4,933,507.76 200,000.00 10 4,933,507.76 5,294,815.47 262,417.33 5,032,398.14 200,000.00 11 5,032,398.14 5,400,948.13 268,977.76 5,131,970.36 200,000.00 12 5,131,970.36 5,507,812.57 275,702.21 5,232,110.36 200,000.00 13 5,232,110.36 5,615,286.37 282,594.76 5,332,691.61 200,000.00 14 5,332,691.61 5,723,233.73 289,659.63 5,433,574.10 200,000.00 15 5,433,574.10 5,831,504.40 296,901.12 5,534,603.27 200,000.00 16 5,534,603.27 5,939,932.49 304,323.65 5,635,608.84 200,000.00 17 5,635,608.84 6,048,335.24 311,931.74 5,736,403.50 200,000.00 18 5,736,403.50 6,156,511.65 319,730.04 5,836,781.61 200,000.00 19 5,836,781.61 6,264,241.00 327,723.29 5,936,517.71 200,000.00 20 5,936,517.71 6,371,281.32 335,916.37 6,035,364.95 200,000.00 21 6,035,364.95 6,477,367.67 344,314.28 6,133,053.39 200,000.00 22 6,133,053.39 6,582,210.38 352,922.14 6,229,288.24 200,000.00 23 6,229,288.24 6,685,493.03 361,745.19 6,323,747.84 200,000.00 24 6,323,747.84 6,786,870.43 370,788.82 6,416,081.61 200,000.00 25 6,416,081.61 6,885,966.30 380,058.54 6,505,907.76 200,000.00 26 6,505,907.76 6,982,370.90 389,560.00 6,592,810.90 200,000.00 27 6,592,810.90 7,075,638.44 399,299.00 6,676,339.43 200,000.00 28 6,676,339.43 7,165,284.22 409,281.48 6,756,002.74 200,000.00 29 6,756,002.74 7,250,781.71 419,513.52 6,831,268.20 200,000.00 30 6,831,268.20 7,331,559.27 430,001.35 6,901,557.91 200,000.00 31 6,901,557.91 7,406,996.68 440,751.39 6,966,245.29 200,000.00 32 6,966,245.29 7,476,421.47 451,770.17 7,024,651.30 200,000.00 33 7,024,651.30 7,539,104.87 463,064.43 7,076,040.44 200,000.00 34 7,076,040.44 7,594,257.52 474,641.04 7,119,616.48 200,000.00 35 7,119,616.48 Real ending value = 7,119,616.48/(1.025^35) = 3,000,000.39

Well, I don’t if the question requires as much complication, but these are my rules for solving for required returns: - Treat the question like a typical TVM - Ready to construct cash flows of more than one year before solving for the required rate of return