# Time Value of Money Chart

This problem involves a contract where someone receives money every few months for a certain length of time and then wants to sell the contract for an arbitrage oppurtunity.

Anyone can buy or sell a contract that entitles the owner (buyer) to receive $80.00 every six months for the next two years (payments made at the end of each period). When the buyer receives the final $80.00 payment, she or he will receive an addition $1,000. The cash flow is shown in the table below.

Today 6 months 12 months 18 months 24 months

$80.00 $80.00 $80.00 $80.00 + $1,000

The rate of return you require to invest in such a project is an 8.0 APR compounded semi-annually. It's 8.0% since there is an alternative investment account available to you which pays an 8.0 APR compounded semi-annually. The price of the contract is $1,200.

a. In the table below, you can report future withdrawals, interests-rate payments, and ending balances for each period following a deposit made, today, into your alternative investment account. Use this table to show me how you could earn an arbitrate profit by selling the contract.

Today 6 months 12 months 18 months 24 months

Deposit

Interest payment

withdrawal amount (This is the amount required to pay the buyer of the contract)

ending balance for period

b. What is the no-arbitrage price of the contract described above (i.e., what is the fair value of the contract?)

c. Prove this by using the same accounting table below, that your answer to part b is indeed the fair value of the contract (i.e., you would only break even if you sold the contract).

Today 6 months 12 months 18 months 24 months

Deposit

Interest payment

withdrawal amount (This is the amount required to pay the buyer of the contract)

ending balance for period

https://brainmass.com/business/the-time-value-of-money/time-value-money-chart-35375

## SOLUTION This solution is **FREE** courtesy of BrainMass!

The completed file is attached. We have calculated interest at 8% p.a. and filled the table. In the first case the deposit gives a higher value of 64.11 which is the profit from the arbitrage.

In b. we have to calculate the fair price of the contract. We reduce the profit. Since the profit is made at the end of 24 months, we find the present value by multiplying by 1/(1.08)^2 which is 54.96 and the value of contract as 1145.036.

In c we fill the table again with this value and arrive at zero balance at the end of the period.

https://brainmass.com/business/the-time-value-of-money/time-value-money-chart-35375