Question

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iu FINS1613 The Perpetuity of Broken Dreams Practice Problem Question 1 The Perpetuity Of Broken Dreams is an investment that pays monthly cash The first payment of $375.00 is due in one month. Payments then grow by 6.0% per month until month 50. The payrnent in month 57 is $423.75, which is 13.0% larger than the original first cash flow of $375.00. Payments then grow again by 6.0% per month until month 112. This pattern of a cash flow followed by 55 periods of growth, which is then followed by a lower cash flow ( that is 13.0% bigger than the last 'lower cash flow') and then subsequent growth, repeats in perpetuity. What is the total present value today at t-0 of the perpetuity's payments if the discount rate is 15.6% EAR? tperioah call a. $244,664.01 b. $266,266.67 c. $298,618.11 d. $284,945.76 e. $226,255.75 5 (1,156丿ー-1=4.21S l. 06 2s-401.sg0 021s-D.LG6 s 012 IS Question 2 s 308.021 onis 2.75 56 . onis The Perpetuity Of Broken ams is an investment that pays monthly cash flows. The first payment of $900.00. lue in one month. Payments then grow by 4.1% per month until month 37. The p, rent in month 38 is S1.071 .00, which is,190% larger than the original first cash flo of $900.00. Payments then grow again by 4.1% per month until month 74. This p\tern of a cash flow followed by 36 periods cash flow ( that is 19.0% bigger than

Answer 1

EAR = 15.6% so monthly interest rate = (1+ 15.6%)^(1/12) - 1 = 1.215%

Calculate the present value of the 1st stream of payments ie. from month 1 to month 56:

P = 375; g = 6%; r = 1.215%; n = 56

Using PV of growing annuity formula

7 1-1 1

PV = 375/(1.215% - 6%) [ 1- ((1+6%)/(1+1.215%))^56] = 96,276.25

Now, this is the PV for the 1st cash flow stream. 2nd cash flow stream will have a PV of 96,276.25*(1+13%) at the end of month 56, and so on, till perpetuity. It can be represented as shown below, growing at 13% every 56 months:

Months (m)	0	56	112	168
PV of cash flow stream	96,276.25	108,792.17	122,935.15	138,916.72

Discount rate for 56 months d = (1 + 1.215%)^56 -1 = 96.70%

PV of cash flow streams from month 56 onwards = CF56/(d - 13%)

= 108,792.17/(96.70% - 13%) = 129,979.49

Total PV = 96,276.25 + 129,979.49 = 226,255.75 (option E)