# Present Value of Bonds and Time Value of Money

Apply the concept of present value to Accuracy. Suppose Accuracy is selling a bond that will pay you $1000 in one year from today. Keep in mind that if Accuracy has financial difficulties in one year you might not get your full $1000 back. Given that a dollar one year from now is always worth less than a dollar today, you most certainly would not pay a full $1000 for this bond.

Given the concepts of the time value of money, answer the following questions in a two to three page response:

1. How much would you pay for an Accuracy bond today? Take into consideration personal risk preferences, interest rates, inflation, and the probability that Accuracy will not be able to pay you back in one year. Note: no need for any math equations for this part. Just explain how much you would personally pay for a $1000 bond for Accuracy and why.

2. Based on your answer to the previous question, what would be your discount rate for this bond? Use the present value formulas to show your work.

3. Pick two other companies in the same industry as Accuracy. One should be one that you would pay less for a $1000 bond than you would from Accuracy and another one that you would pay more for a $1000 bond compared to from Accuracy. Explain why you would pay more or less for their bonds.

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#### Solution Preview

1. A dollar worth today is more than a dollar worth one year from today. The bond which is being sold by Accuracy would provide $1000 one year from now. However, it is uncertain, due to company's financial situation whether the investor would get full $1000 back. Hence, the decision to buy this bond now would depend on a number of adjusting factors such as personal risk preference, inflation, interest rates, and the probability that Accuracy would not be able to pay back in one year. If the simple concept of time value of money is applied, the value of $1000 today would be less than the value one year from now. So, depending on the discount rate the amount worth today would come out to be less than $1000. Depending on following factors, it could be further below the discounted value.

Personal Risk Preference: A safe dollar in hand is better than risky dollar which is not there in hand. Hence, if the investment promises to pay more than $1000, then some amount of risk can be taken as a premium for risk bearing. However, in the absence of this additional compensation, a safer dollar is better than risky one.

Interest Rate: The prevailing interest rate would provide at least that much return above the initial investment. If the amount paid by the company is less than the prevailing interest rate in the market, then the bond could be bought at a much lower price.

Inflation: The bond should be able to cover the inflation ...

#### Solution Summary

This solution provides a detailed discussion on the time value of money in 900 + words, including 5 references. This includes at least one page on the quantitative and qualitative drivers behind valuing the Accuracy bond, provides calculations using the present value formula for determining the appropriate discount rate, and discusses the price for the bonds of two other companies in the same industry.