A cash flow series is increasing geometrically at the rate of 8% per year. The i

Question

A cash flow series is increasing geometrically at the rate of 8% per year. The initial payment at EOY 1 is $5,000, with increasing annual payments ending at EOY 20. The interest rate is 13% compounded annually for the first six years and 5% compounded annually for the remaining 14 years. Find the present amount that is equivalent to this cash flow.

5 PERCENT TABLE

8 PERCENT TABLE

13 PERCENT TABLE

08200|0 8 7 7 5-4 8 503-37572 nP_0 7 7 2 1724090 2 6 1 628520 e/ 5 3 6 8 3-9 7 5 4 2-2 1 0 0 9-9 8 8 8 8 v to-nd ceF|OG -1 0 0 0 0-0 0 0 0 0-0 0 0 0 0 0 0 0 0 0 9 ndod 08200|0 8 7 7 5-4 8 503-37572 409|02616|2 8 520 097|76554|4 3 3 3 3 07721-7 08138-4 G -1 0 0 0 0000000000000000 4420574287|4 4 4 4 444444 29369-5 6 3 7 1-2 2 2 2 2 2 2 2 2 2 5 5 2 4 2-7 8 6 0 2-5 5 5 5 5-5 5 5 5 5 ehFvP-9 8 7 530 7 4 1 79 9 9 9 9-9 9 9 9 9 01234556770 0 0 0 0-0 0 0 0 0 00516-901 00205-129 0 5 5 1 2044 69-8 1066-5 4 4 0 0 67-6 7 388-70296 336 e 2975 aFvF_0 0 1 3 58150 3. 3.·12-4 5 7 9 135803 1112|22233 12345- 11-1 40875|27869-78310|13579 3-6 0 6 43|46051|8 6 5 56 8-4 1 7 4 1-85308|53197 ehFvP-9 9 8 8 777666|5 5 5 5 444433 05653|1 1 5 3 9-3 9699-90603 18-05598-22673 52-19877-89025 01122|3 4 4 5 6-7 7890|12456 02756-07 50517-40 or AF-To G -1 1 1 1 1-1 1 1 1 1-1 1 1 1 2 2 2 2 2 2 0-1 2 3 4 5 6 7 8 9 0 N1 2 3 4 5-6 7 8 9

Explanation / Answer

Solution:

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A B C D E F G H I J K L M N O P Q R S T 1 Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 2 Cash Flow with geometrical rate of 7%= Cash flow*(1+9%)^(Years-1) 4000.00 4360.00 4752.40 5180.12 5646.33 6154.50 6708.40 7312.16 7970.25 8687.57 9469.45 10321.71 11250.66 12263.22 13366.91 14569.93 15881.22 17310.53 18868.48 20566.65 3 Discount rate for last 13 years 4% 4 Terminal Value $123,025.98 Using excel formula = NPV(A3,H9:T9) 5 Total Value 4000.00 4360.00 4752.40 5180.12 5646.33 6154.50 129734.38 (= Cash flow at year 8 + Terminal value at year 8) 6 Discount rate of Frst 7 years 16% Present value $63,712.27 Using Excel Formula=NPV(A6,A5:H5)

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