Present Value 2 Some common accounting examples Example 1: XYZ company has sold goods in exchange for a non-interest bearing note receivable. The note is in the amount of $6,000 and is due in two years. XYZ requires a rate of return of 10% on notes of this type. How much revenue should be recognized in the current year? This is an example of a single sum present value problem: = $6,000 * PV(10%, 2) X $6,000 * .82645 =X $ 4,958.70 = X = revenue and net (less discount) note receivable This would then be recorded as follows: dr. Note receivable 6000 cr. Revenue 4958.7 cr. Discount on note receivable 1041.3 On the balance sheet: Note receivable (net of discount) 4958.7 What happens to the discount? It becomes interest income in each of the two years. (You did not really believe that the company would not charge interest, did you?) using straight line amortization: end of year 1: dr. discount 520.65 cr. Interest income 520.65 at the end of the first year the note will now appear on the balance sheet as follows: Note receivable (net of discount) 5479.35 Example 2: Bond issuance XYZ company is issuing bonds with a face value of $ 100,000. The bonds pay 10% interest and mature (the principal will be paid) in 5 years. Interest is paid semi- annually. How should the bonds be recorded on the balance sheet? That depends on how much money the company actually receives for the bonds. And that, in turn, depends on how much investors (the market) want to earn on an investment of this type. Case 1: Bonds are issued at par (face value) If investors want to earn 10%, then the following calculation will take place: Principal coupon Interest semi-annual rate payment payment $100,000 10% $10,000 $5,000 Bonds are discounted at 5% (10% compounded semi-annually): 100000 PV(5%, 10) 0.61391 $61,391 5000 Pva(5%,10) 7.72173 $38,609 $100,000 to record the bond issue: dr. cash $100,000 cr. Bonds payable $100,000 Case 2: What if the market wants to earn 12% (or 6% semi-annually)? 100000 PV(6%, 10) 0.55839 $55,839 5000 Pva(6%,10) 7.36009 $36,800 $92,639 Bonds are issued at a discount to record the bond issue: dr. cash $92,639 dr. discount $7,361 cr. Bonds payable $100,000 Case 3: What if the market wants to earn only 8%? 100000 PV(4%, 10) 0.67556 $67,556 5000 Pva(4%,10) 8.1109 $40,555 $108,111 Bonds are issued at a premium to record the bond issue: dr. cash $108,111 cr. Bonds payable $100,000 cr. Premium $8,111 What happens to the premium or discount? It will be amortized as part of interest expense. Example III Which is the better choice? Cash or a note payable? XYZ company is negotiating with WWW company to purchase equipment. WWW offers the alternatives: The equipment could be purchased for $100,000 cash or XYZ could pay $ 108,000 in one year. XYZ can earn 12% on its investments. Equation: Amount PV(12%,1) Present value $108,000*PV(12%,1) $108,000 0.89286 $96,429 < $100,000 XYZ should sign the note and in the meantime invest the $100,000 at 12%. What if XYZ cold earn only 6% on its investments? Present value 108000 x PV (6%, 1) 108000 0.9434 101887.2 > 100000 XYZ shold pay the $100,000 now. Example IV Buying a car (you will not need this for either accounting 200, 300 or 301) The car could be purchased for cash $30,000 or for 5 annual payments of $7,514. The payments are to be made at the end of each of the next five years. What is the interest rate that is being charged? 30,000 = $7,514xPVa(x%,5) 30,000/7.514 = 3.9925472 look up in the PV table for 5 periods and determine that the interest rate is 8% Or the question could be asked as follows: You could either pay $30,000 now or make 5 payments, at 6%. What would be the amount of each payment (end of the year!) 30,000/Pva(6%,5) = X Pva(6%,5) annual payments 30000 4.21236 $7,121.90 Obviously, car payments are made monthly, but, once you understand the principle involved, you use a finacial calculator or a computer to calculate the payments or annual interest rate.