Question

Dobson Construction has an investment project that would cost $150,000 today and yield a one-time payoff of $167,000 in three years. Among the following interest rates, which is the highest one at which Dobson would find this project profitable?a. 7%

b. 6%

c.5%

d. 4%

Answer 1

Correct answer to this question is none of them. But if you reduce the time period to 2 years the answer would be:

C) 5%.

Explanation:

First of all, let me explain that, when project goes profitable and when it is considered non-profitable or at loss.

The basic indicator is through PV or Present Value of yield calculation. So, here is the formula to calculate Present Value or PV:

PV =
`FV*(1+i)^(-n)`

where,

FV = Future Value

i = annual interest rate

n = period

So, if this PV of yield is greater than initial money that have been invested than project is predicted to be profitable. Let's calculate for all options.

At option a) i = 7% = 0.07

PV= 167,000*
`(1+0.07)^(-3)`

PV = 136321.7454

At option b) i = 6% = 0.06

PV= 167,000*
`(1+0.06)^(-3)`

PV = 140216. 4203

At option c) i = 5% = 0.05

PV= 167,000*
`(1+0.05)^(-3)`

PV = 144260.879

At option d) i = 4% = 0.04

PV= 167,000*
`(1+0.04)^(-3)`

PV = 148462.3919

Here, you can clearly see that, for three years time period, all of the options are incorrect as none of the interest rate gives the PV value greater than initial investment which is 150,000 dollars hence, at 3 years time period project will be at loss for all these options.

But if you reduce the time period to 2 your correct answer would be C) 5%.

the PV is higher at 5% and 4% the highest interest rate at the project is profitable is 5%

Answer 2

Dobson will be profitable at an interest rate ≤ 4% hence the closest answer is ( D ) Note : the investment can be profitable when the (Pv) is greater than the cost of investment

Step-by-step explanation:

cost of investment project = $150000

yield time = 3 years

yield value = $167000

at what interest rate will this be profitable for Dobson construction APPLYING this equation

Pv = fv * ( 1 + i ) ^ (-n)

fv = project yield

i = interest rate

n = time ( number of years ) = 3

Pv = present value

considering all given interest rates

for i = 7% = 0.07

Pv = 167000 * ( 1.07 )^( - 3 )

Pv = 167000 * 0.8163 = $136322

for i = 6% = 0.06

Pv = 167000 * ( 1.06 )^(-3)

Pv = 167000 * 0.8396 = $140213

for i = 5% = 0.05

Pv = 167000 * (1.05)^(-3)

Pv = 167000 * 0.8638 = $144254

for i = 4% = 0.04

Pv = 167000 * (1.04)^(-3)

Pv = 167000 * 0.8890 = $148463

Note : the investment can be profitable when the (Pv) is greater than the cost of investment