Completion of Accounting Chapter Summaries

ACC 201: Essentials of Accounting

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Chapter 8: How do you handle Opportunity Cost of Capital and Operational Risk?

So far in the IV analysis, we have assumed that the opportunity cost of capital is zero. This is an unreasonable assumption because there are always alternative uses for capital.

What is the impact of an opportunity cost of capital in the IV Value Analysis? It will decrease the IV, even make it negative.

Time value of money comes into play

Suppose you have excess capital and an opportunity to earn a 5% return on your capital.

How much will a dollar invested today will become after:

1 year? = 1.00 capital + 1.00 x 0.05 interest = 1.00 x (1 + 0.05) = $1.05

when you have the opportunity to make returns, this one dollar becomes more important

2 years? = 1.05 capital + 1.05 x 0.05 interest = 1.05 x (1 + 0.05) = 1.05^2 = $1.1025

3 years? = 1.05^2 capital + 1.05^2 x 0.05 interest = 1.05^2 x (1 + 0.05) = 1.05^3 = $1.157625

Which will you prefer - receiving a dollar today or $1.157625 after 3 years? Indifferent

In other words, the present value of $1.157625 after 3 years is a $1.00 today.

What then will be the present value of a dollar after 3 years? = 1/1.05^3 = $0.863838

What then is the present value of a dollar after n years? = 1/1.05^n

Suppose the opportunity cost of capital is r% and a dollar is received after n years:

What will be the present value of this dollar? = 1/(1 + r)^n

What will be the present value of X dollars received after n years? = x/(1 + r)^n

What will be the present value of $2,000 received after 3 years with an OCC of 5%?

= 2,000/(1.05)^3 = $1727.675

How should IV Analysis be modified to accommodate for opportunity Cost of Capital?

Recognizing the time value of money, convert all future cash flows into their present values.

Find the Net Present Value by calculating the (PV of _____ – PV of _____ ) of each option.

Choose the option with the highest positive NPV, if all NPV are negative, then choose the _______ .

NPV is the _______ _______ the decision maker earns beyond the return implied by the O.C.C.

Suppose the opportunity cost of capital is 6%, what is the present value of $1,000 after 9 years?

$591.8985

Now suppose that there is some uncertainty in receiving the $1,000 after 9 years. That is there is a chance that you might NOT receive the $1,000 in the future. How much will you value today this uncertain $1,000 after 9 years?

Less than $591.8985 Equals to $591.8985 More than $591.8985

Suppose the present value of this uncertain $1,000 for you is only $500.249, the risk premium equals $91.6495, or equivalently the risk adjustment to the discount rate is 2% because the PV of $1,000 after 9 years discounted at 8% equals $500.249.

What factors play into the risk adjustment?

_______

_______

_______

How should the NPV Analysis be modified to account for the Operational Risk? ___________________

What do you do when you are unsure about the exact level of risk adjustment? __________________________

What can you learn from the IRR (Internal Rate of Return) of a business or project? _____________________

How does one use IRR to decide whether to invest in the business or not? _________________________