Question

You are the chief financial officer of a firm. The firm has an expected liability (cash outflow) of $2 million in ten years at a discount rate of 5%.

Calculate the amount the firm would need on the present date as savings to cover the expected liability.

Calculate the amount the firm would need to set aside at the end of each year for the next ten years to cover the expected liability.

Explain the specific business decision that management made after computing this value. Analyze how management used the concept of the time value of money principles to make this decision.

Analyze factors other than the time value of money that management considered or should have considered in reaching the business decision.

Answer 1

P.V. = FV/(1+r)ⁿ = 2/(1.05)¹⁰ = $1.23 million

Where FV = future value

PV= present value

r = discount rate

= number of periods

The amount that the firm would need on the present date as savings to cover the expected liability is $1.23 million.

The amount the firm would need to set aside at the end of each year for the next ten years to cover the expected liability is: 2/10 = 0.2 million

If the firm decides to deposit a particular amount in a sinking fund every year for the next ten years and the return on deposit is 5% then the amount to be deposited will be

FVA = A [{(1+r)ⁿ -1}/r]

where FVA = future value of annuity

A = annuity amount

r= discount rate

n= number of periods

2= A[{(1.05)¹⁰-1}/0.05]

2=12.58 A

A = 2/12.58 = $0.159 million

Now if the firm goes for the option of depositing in sinking funds every year then the firm would be able to save more per year as then it would need to keep aside $0.159 million per year to meet the liability and otherwise it would require $0.2 million per year to meet the liability.

This happens because when the firm will deposit money in a sinking fund it will earn a return on that deposit and that return will also be reinvested into the fund. An investment of a rupee today would grow to 1.05 rupee in a year so it is better to invest money in the sinking fund. Also the value of $1.23 million today will be 2 million in 10 years so it is better to start saving today.