Question

Find the present value of the following cash flow stream assuming a discount rate of 8%: A payment of $10,000 received at the end of each MONTH over the coming 4 years, followed by a payment of $5000 received at the end of each MONTH over the 6 years after that.

a.) $556,975.15

b.) $409,619.13

c.) $285,172.61

d.) $207,297.84

e.) $616,916.97

Answer 1

Questions ask to calculate the present value of the given series.

Given rate = 8% [ Assuming APR]

Cash flows are in monthly frequency so you need monthly rate. For this calculate periodic rate.

Rate = 8/12 = 0.666667%

For the calculation of PV we calculate the PVs in separate series

1. Calculate PV of $10000 monthly Annuity for 4 years or 48 months

PV = Annuity x cumulative discounting factor @0.666667% for 48 periods

or if you have financial calculator then put vaues in TVM as N=48, I/Y=0.66667%, PMT = 10000, FV=0

Compute PV = 409619.1296

2. Calcuate the PV at Time 4, of 2nd Series of $5000 for next 6 years or 72 months

PV at Time 4 =  Annuity x cumulative discounting factor @0.666667% for 72 periods

or

if you have financial calculator then put vaues in TVM as N=72, I/Y=0.66667%, PMT = 5000, FV=0

Compute PV = 285172.6107

Above Pv at Time 4. Now calculate the pv at Time 0 by discounting this value 4 years back.(48 months)

PV = 285172.6107(1.00666667)⁴⁸

PV = 207297.8463

3. Combined Step 1 and Step 2 PV

409619.1296 + 207297.8463

= 616916.97 approx

So option D is correct