Question

Question 3. (/5) Alibaba group is setting aside capital to fund an environmental protection project. Funds earmarked for the project will accumulate at the rate of $50 000 per month until the project is completed in two years. Once the project starts, costs will be incurred at the rate of $150 000 per month over 24 months. Alibaba currently has $250 000 saved. What is the minimum number of months the Alibaba group will have to wait before the group can start the project if money is worth 24 percent nominal, compounded monthly? Assume that 1) Cash flows are all at the ends of months 2) The first $50 000 saving occurs one month from today 3) The first $150 000 payment occurs one month after the start of the project 4) The project must start at the beginning of a month

Answer 1

There are following steps to solving this question:

1. Find the PV of the project payments at the beginning of the project
2. Find the time it takes to accumulate the deposit and current savings to accumulate to the PV calculated in part 1

1) We are given the following information:

PMT	$        1,50,000.00
r	24.00%
n	2 years or 24 months
frequency	12 (Monthly compounding)

We need to solve the following equation to arrive at the required PV:

1-(1+ -)-пхirequency frequency PV = PMTX frequency

1-(1 +0:24)-2x12 PV = 150000 x

PV = 2837088.84

So we need to accumulate $2837088.84 on the date of beginning of the project

2) Now we find the time take to accumulate this amount:

We are given the following information:

PMT	50000
r	24.00%
PV	250000
T	12
FV	$28,37,088.84

We need to solve the following equation to arrive at the required n:

FV = PMT x (1+4)nx?' – 1 + PV x (1 + " } nx 12

2837088.84 = 50000 x (1 + 0.24)nx12_1 - + 250000 X (1+

n = 2.80

So if will take approximately 2.80 years to accumulate the required amount so Alibaba should wait for 2.8 years