Assume that you will receive $2,000 a year in Years 1 through 5,$3,000 a year in Years 6 through 8,and $4,000 in Year 9,with all cash flows to be received at the end of the year.If you require a 14 percent rate of return,what is the present value of these cash flows? (Round to the nearest whole dollar)
A) $9,851
B) $13,250
C) $11,714
D) $15,129
E) $17,353

Question

Quizplus · Accepted Answer

Step 1 - The first two cash flows can be considered annuities, so take the present value of each cash flow as an annuity.
PV = PMT × 11ea7fdb_fc1d_860f_a768_6bd666b0d14f_TB2902_11 PV = 2,000 × 11ea7fdb_fc1d_8610_a768_7bf916e3cb36_TB2902_11 = $6,866.16
Using a financial calculator:
N = 5, I = 14, PMT = -2,000, FV = 0, cpt PV = $6,866.16
PV = 3,000 × 11ea7fdb_fc1d_8611_a768_afaa20737061_TB2902_11 = $6,964.90
Using a financial calculator:
N = 3, I = 14, PMT = -3,000, FV = 0, cpt PV = $6,964.90
Step 2 - The second cash flow still needs to be discounted back to today from year 5.
PV = 11ea7fdb_fc1d_8612_a768_25df6d9c3c02_TB2902_11 PV = 11ea7fdb_fc1d_8613_a768_bdabbeeaf4c1_TB2902_11 = $3,617.35
Step 3 - Find the present value of the last cash flow.
PV = 11ea7fdb_fc1d_ad24_a768_b305e81655dc_TB2902_11 = $1,230.03
Step 4 - Add all of the present values together.
6,866.16 + 3,617.35 + 1,230.03 = $11,713.54

Assume That You Will Receive $2,000 a Year in Years