CAPITAL BUDGETING

CAPITAL BUDGETING

TIME VALUE OF MONEY ISSUES

By William M. Holmes, Ph.D.

Capital assets and liabilities are things that have an expected life over one year.

Time Value of Money refers to the appreciation or depreciation of the value of a capital asset over time. Some assets increase in value. Some decrease in value.

Loans are capital liabilities that appreciate over time, due to interest rates.

Investments are capital assets that appreciate over time, due to inflation.

Loans

P=present value of loan

F=future value of loan (total amount to be paid back, principle plus interest)

N=number of payments

F=P(1+i)^N

If you borrow $50,000 at 6% interest, the value to be paid back over 5 years would be:

F=50,000(1+.06)⁵ = 50,000 x 1.338 = 66,911.

The yearly payment would be $13,382 ($66,911/5).

Investments

The same principles apply to investments.

If you invest $10,000 and expect to earn 5% per year on it, the expected value after 10 years would be:

F=10,000(1+.05)¹⁰ = 10,000 x 1.6399 = $16,399

A gift of $10,000 now is equivalent to a promise of $16,399 ten years from now.

Or, P=(F/(1+i^N), to calculate the present value of a future gift. If the gift is 10,000 in five years, the present value of it is (assuming 5% interest)

P=10,000/(1+.05⁵)=10,000/1.276 = 7,837

A promise of 10,000 in five years is worth $7,837 today.

Appreciating Assets

Land, artwork, collectables, antiques, bonds, CD’s, some stocks, annuities

Depreciating Assets

Office equipment, vehicles. Note: some assets depreciate according to Straight Line method (linear distributed over time period), rather than Compound method (accelerated distributed over time period). Less expensive capital assets (less than $12,500) may be written off as a one-year business expense.

Stable Assets

CD’s, Notes

Variable Assets

Buildings, Bonds

Uncertain Assets

Good will of donors, interest of stakeholders, and importance of capital asset to mission of organization

EVALUATING ALTERNATIVE INVESTMENTS

Four methods: net present cost, annualized cost, net present value, and internal rate of return.

When alternatives have same life expectancy and cost is the only major consideration, Net Present Cost is used. To calculate Net Present Cost, first calculate all costs and revenues for an object over the expected life of the object, Then, calculate the Net Present Value of the item, given its Total Costs at the end of its lifetime.

Suppose one computer costs $1,000 (computer A) and another costs $950 (computer B). Each has a five year life expectancy. The first computer has maintenance costs of $100 per year. The second computer has maintenance costs of $130 per year.

The first year cost is:

Computer A 1,000+100=1,100

Computer B 950+130=1,080

Computer B appears cheaper, even with a higher maintenance cost.

However, the life of the computers is five years.

The total cost of the computer A is 1,000+500=$1,500.00

The total cost of the computer B is 950+650=$1,600.00

Now it appears that computer B is more expensive. However, the maintenance is paid over five years. The money for it has a Time Value. We can calculate the Net Present Cost if we assume an interest rate for the money to be paid out for maintenance. Let’s assume 10%

For computer A, P=1,500/1.10⁵ = 1,500/1.61 = 931.67

For computer B, P=1,6000/1.10⁵= 1,600/1.61 = 993.79

The total dollar outlay for computer B appears higher than A. But this must be discounted to the present value, because most of the maintenance money is paid in future years.

The annual distribution of this would be:

Computer A, 931.67/5 = 186.33

Computer B, 993.79/5 = 198.76

The Net Present Value (first year cost) is:

Computer A, $1,000 +186.33=1,186.33

Computer B, $950 + 198.76 = 1,148.76

Thus, computer B is cheaper over the life of this asset, even though the total cost appears to be greater, because the money to pay maintenance in future years can be invested to earn interest until it has to be paid out.

Annualized Cost Method. Under the annualized cost method, the objects being evaluated may have different lifetimes. The formulas are the same as for Net Present Cost, except different time amounts are used for the compared items. When assets have the same lifetime, the Annualized Cost Method is the same as the Net Present Cost method.

Net Present Value. The net present value method adds in revenues that might be generated by an asset. Sometimes, projects are required to produce net income. The profit rate for this is called the “hurdle rate” or the “required rate of return.” The revenues expected to be earned over the life of the asset (the Total Revenues) are subtracted from the Total Cost, resulting in a Net Total Value. The Net Total Value is then converted to the Net Present Value.

Internal Rate of Return. The Net Present Value approach doesn’t consider the relative profit rate, only the dollar profit rate. The Internal Rate of Return approach converts the dollar profit into percent profit and compares the percentages. An asset is selected if the percent profit is greater, even though the dollar profit is less.