Question

Bau Long-Haul, Inc., is considering the purchase of a tractor-trailer that would cost $281,660, would have a useful life of 7 years, and would have no salvage value. The tractor-trailer would be used in the company's hauling business, resulting in additional net cash inflows of $80,000 per year. The internal rate of return on the investment in the tractor-trailer is closest to (Ignore income taxes.):

Answer 1

rate 20.86%

Step-by-step explanation:

We will setp up the formula for an ordinary annuity

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 80000

time 7

rate = r

`80000 * (1-(1+r)^(-7) )/(r) = 281,660`

To solve we need to do it on excel, with the IRR function or estimate with try and error:

`(1-(1+r)^(-7) )/(r) = 281,660/80,000`

The first part is the annuity factor with n = 7 we need to look into the PV table of an ordinary annuity which comes close to the quotient of 281,660/8,000 = 3,52075

at 20% = 3.605

at 21% = 3.508

The rate is between 20% and 21%

We now sart calculating the factor changing the decimals:

our target is: 3,52075

20.5% 3.5557

20.8% 3.5269

20.9% 3. 5174

Now the rate will be between 20.8%

and 20.9%

we start moving amoung the centimals

20.85% 3.5222

20.86 % 3.5212

20.87 % 3.5203

our target is: 3,52075

the IRR will be between 20.86% and 20.87%

we are almost there, we check if we need to round up or down:

our target is: 3,52075

20.865% 3.5207

20.864% 3.5208

20.866% 3.5206

It will be betwene 0.4 and 0.5 so it is better to round down.

We conclude the IRR is 20.86%