5.4 Business Decisions with Present Value and Bond Valuation

Evaluating Business Decisions with Present Value Techniques

• Sparky is expanding and needs to decide whether to buy or lease a new factory site in Phoenix.
• The decision will be based on which option is the least costly in present value terms.
• Three buildings are under consideration: Buildings A, B, and C.

Building A: Purchase Option

• Purchase price: $500,000$.
• Useful life: 25 years.
• Present value of Building A: $500,000$ because it's an immediate cash outflow.

Building B: Lease Option

• Lease terms: 20 years with annual payments of $59,000$ made at the beginning of each year.
• This is a present value of an annuity due scenario.
• Sparky's estimated cost of funds: 12%.
• No modifications are needed for the interest rate or number of periods since payments are annual.

Calculation

• Annuity Due Factor (12%, 20 periods): 8.36578.
• Present Value of Lease Payments: 59,000 \times 8.36578 = $493,581.
• Building B is a less costly alternative than Building A.

Building C: Purchase with Sublease

• Purchase price: $550,000$.
• Excess space subleased for 10 years with net annual rental income of $12,000$.
• Rental payments received at the end of each year, making it an ordinary annuity.

Calculation

• Ordinary Annuity Factor (12%, 10 periods): 5.65.
• Present Value of Rental Income: 12,000 \times 5.65 = $67,803.
• Net Present Value of Building C: 550,000 - $67,803 = $482,197.
• Building C is the least costly alternative.

Recommendation

• Recommend purchasing Building C, provided Sparky is comfortable being a landlord for the next 10 years.

Valuation of Long Term Bonds Payable

• Bonds make two promises: repayment of principal at maturity and periodic interest payments.

Bond Promises

• Repay Principal (Face Value): Single sum payment at maturity.
• Pay Periodic Interest: A series of equal payments (annuity).
• Interest payments are typically made annually or semi-annually (ordinary annuity).

Example Scenario

• A company issues a five-year bond with a face value of $500,000$.
• Promise to pay $500,000$ at the end of year five.
• Promise to pay periodic interest payments over the five-year term.

Establishing the Selling Price of a Bond

• Determine the present value of the face value (single sum).
• Determine the present value of the series of interest payments (ordinary annuity).
• Sum these present values to determine the selling price of the bond.

Formula

• Selling Price = Present Value of Face Value + Present Value of Interest Payments
• Present Value of Face Value = Face Value \times Present Value of a Dollar Factor (using market rate and number of periods)
• Present Value of Interest Payments = Interest Payment \times Present Value of Ordinary Annuity Factor (using market rate and number of periods)

Variables

• $FV$ = Face Value of the Bond (e.g., $500,000$)
• Payment = Dollar amount of interest payment, calculated as Face Value \times Stated Rate

Interest Rates

• Market Rate of Interest: The rate creditors demand based on the company's creditworthiness.
• Stated Rate of Interest: The rate the company promises to pay on the face value of the bond, used to determine the periodic interest payment.
• Because interest rates and creditworthiness change over time, these two rates are usually different.

Terminology

• Market Rate: Also known as the effective rate or yield.
• Stated Rate: Also known as the coupon rate; explicitly written on the bond agreement.

How Bonds Sell

• Bonds can sell at par, at a discount, or at a premium depending on the relationship between the stated rate and the market rate.

Selling at Par

• Stated Rate = Market Rate
• Present Value of Cash Flows = Face Value
• No premium or discount.

Selling at a Discount

• Stated Rate < Market Rate
• Present Value of Cash Flows < Face Value
• The difference is the discount on the bond payable.

Selling at a Premium

• Stated Rate > Market Rate
• Present Value of Cash Flows > Face Value
• The difference is the premium on the bond payable.