-500412667&questionld-228 DHolcomb-Business Finance 3310-00s: MW 9-(1) Stephanie

Question

-500412667&questionld-228 DHolcomb-Business Finance 3310-00s: MW 9-(1) Stephanie Hernandez & s Homework: Homework 3 k Score: 0 of 10 pts P6-28 (similar to) $44,000 per payment. The first $44, ess Fi phanie Hernandez 17 of 22 (21 complete) HW Score: 90 15%, 198 33 of 220 pts -Question Help * npts a value of annuity payments) The state lottery's milion-dollar payout provides for $1.1 million to be paid in 25 installments of present value of this stream of cash flows? If 14 percent is the discount rate, what is the present value of the cash flows? 000 payment is made immediately, and the 24 remaining $44,000 pa yments occur at the end of each of the next 24 years. If 7 newo 6/18 5/18 0% (1 s the present value of the annuity due is (Round to the nearest cent) ue Qu Ine pr (10/10) (10/10) 2 (10/10) 6 (10/10) o (0/10) (RJ) , More Enter your answer in the answer box and then click Check Answer

Explanation / Answer

Answer for a = $548,650.70

Answer for b = $344,746.04

Calculations and explanations are shown below:

a. Here the annuity amount is $44,000 and hence present value of the annuities are = 44,000 + Present value of annuities of 44,000 for 24 years discounted at 7%. This makes it an annuity due as each payment can be regarded as being made at the start of the year i.e. the 1st payment now, 2nd payment at the start of 2nd year, 3rd payment at the start of 3rd year and so on.

Thus the present value is shown in the table below:

b. In this case the discount rate is 14%. Hence present value of the annuity due is:

Year Amount 1+r PVIF PV 0 44,000.00 1.070 1.0000 44,000.00 1 44,000.00 0.9346 41,121.50 2 44,000.00 0.8734 38,431.30 3 44,000.00 0.8163 35,917.11 4 44,000.00 0.7629 33,567.39 5 44,000.00 0.7130 31,371.39 6 44,000.00 0.6663 29,319.06 7 44,000.00 0.6227 27,400.99 8 44,000.00 0.5820 25,608.40 9 44,000.00 0.5439 23,933.08 10 44,000.00 0.5083 22,367.37 11 44,000.00 0.4751 20,904.08 12 44,000.00 0.4440 19,536.53 13 44,000.00 0.4150 18,258.44 14 44,000.00 0.3878 17,063.96 15 44,000.00 0.3624 15,947.62 16 44,000.00 0.3387 14,904.32 17 44,000.00 0.3166 13,929.27 18 44,000.00 0.2959 13,018.01 19 44,000.00 0.2765 12,166.37 20 44,000.00 0.2584 11,370.44 21 44,000.00 0.2415 10,626.58 22 44,000.00 0.2257 9,931.38 23 44,000.00 0.2109 9,281.66 24 44,000.00 0.1971 8,674.45 Total 548,650.70

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