Question

In: Economics

A construction company needs enough money to purchase a new tractor-trailer in 6 years at a...

A construction company needs enough money to purchase a new tractor-trailer in 6 years at a cost of $450,000.

If the company sets aside $175,000 in year 2, $125,000 in year 3, and $75,000 in year 4, how much will the company have to set aside in year 5 to have the money needed in year 6?

Assume investments earn 8% per year compounded semi-annually.

What is the value of the individual cash flow at year = 1?

What semi-annual interest rate do you use to solve for the unknown cash flow in year 5?

What is the numerical value for the amount of funding the company have to set aside in year 5 to have the money needed in year 6?

Solutions

Expert Solution

Money needed at end of year 6 = $450,000

Savings at the end of year 2 = $175,000

Savings at the end of year 3 = $125,000

Savings at the end of year 4 = $75,000

Rate of interest = 8% compounded semi annually

There is no saving being made at the end of year 1 to purchase new tractor.

At 8% annual rate, semi annual rate would be [1 + (0.08 / 2)]2 = 8.16%

Money saved in year 2 will be saved for 4 years which makes 175,000 worth 175,000 [1 + (0.08 / 2)]8 = 239,499.58 after 4 years.

Money saved in year 3 will be saved for 3 years which makes 125,000 worth 125,000 [1 + (0.08 / 2)]6 = 158,164.87 after 3 years.

Money saved in year 4 will be saved for 2 years which makes 75,000 worth 75,000 [1 + (0.08 / 2)]4 = 87,739.39 after 2 years.

Lets say money saved in year 5 is $X. Money saved in year 5 will be saved for 1 years which makes X worth X [1 + (0.08 / 2)]2 = 1.0816X after 1 year.

Total amount in year 6 becomes = 239,499.58 + 158,164.87 + 87,739.39 + 1.0816X = 450,000

As money saved in year 2 / 3 / 4 is valuing more than the purchase price of tractor in year 6. They do not need to save anything in year 5 for this.

Rahul Sunny answered 8 months ago
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