•A dollar today is worth more than a dollar tomorrow
•Opportunity cost related to having cash at different points in time
•Basic computations to reflect this
–Single period flow (see table on page 131)
–Annuity (see table on page 132)
When determining Time Value of Money need to answer these two questions:
1) What is the interest rate we are assuming?
2) How far into the future?
Single period flow computation for TVM
Present value of $1 received at the end of period n at an interest rate of i%
Annuity for TVM
We have uniform flows of money
Figures Are Cash Flows
•You can spend cash
•You cannot spend income
•You can earn interest on cash
•You cannot earn interest on income
When Do Flows Occur?
•Present value computations assume flows occur at end of period
•Compounding occurs at end of period
•In most problems we will assume that the period is a
Complexities with Present Value
- Taxes and depreciation tax shield
- If flows occur during the year
- Discount Rates
Taxes and Depreciation Tax Shields
–Reflects tax savings from being able to subtract
depreciation in determining income tax.
- You have to allocate these savings over time-not all at once
- These are cash inflows
Capital Gains =
= Present Market value - book value
= sales price - book value
* When replacing an old product, multiply by tax rate and subtract during year 0
Price per unit x units sold
(Original cost - salvage value) / useful life
Cash flow analysis for year zero
((negative)cost of new machine) + present market value of old machine - (capital gain x tax rate)
Cash flow analysis for years 1-4
Rev - VC - Maintenance - property tax = BTNI
BTNI x (1-TR) = ATNI
ATNI + (depreciation x TR) = Cash flow/years 1-3
For year 4, add salvage value
NPV comparison final answer
Multiply each year's CF times given interest rate in table. Add all values together
Add each year's cash inflows to cost. At the end of year 3, you still need 14,500 dollars to pay it off so you divide that amount by year 4's cash inflow and add that fraction value to 3 years to determine total payback time.
If the value is positive, you should do the project. If it is negative, don't do it because you are losing money on cost of capital. If cost of capital is 10%, and NPV is positive, your cost of capital ends up being less than 10%.