Budi Frensidy - FEUI1 Mathematics for Asset Valuation Budi Frensidy Faculty of Economics, University of Indonesia 4 th International Conference on Research and Education in Mathematics Renaissance Hotel Kuala Lumpur, Malaysia October 2009

Budi Frensidy - FEUI2 Introduction Present value concept is needed for:  Project evaluation  Asset valuation (real and financial)  Recording and reporting an asset on the balance sheet  We usually do the discounting one by one by using the basic equation  This method is impractical as the number of periods can be infinite (~)

Budi Frensidy - FEUI3 The Purpose of the Paper  We actually can use the short-cut equations if certain conditions are met namely equal cash flows or equal growth (in percentages)  There are at least 13 other equations besides the basic and continuous equation that can be used for this  This paper tries to enumerate and give examples of all the equations using a simple and interesting case on valuation

Budi Frensidy - FEUI4 Definition of Annuity and Perpetuity  Annuity is a series of cash payments or cash receipts, generally in equal amounts, in equal periodic intervals. Installments on home loan or car loan and bond coupon are some examples  Whereas perpetuity or perpetual annuity is infinite annuity which is a special type of annuity when the periods are countless like stock dividends, pension allowances, royalties, and copyrights

Budi Frensidy - FEUI5 Valuation Case (1) A young investor is contemplating investment in the following financial assets which are offered at the same price i.e. Rp 100 million. With his budget constraint, he can choose one and only one of the alternatives given. a. Zero-coupon bond with the nominal value of Rp 250 million, due in 8 years b. No-par bond that pays cash Rp 18 million every year for 10 times starting next year c. No-par bond that pays cash Rp 16 million every year for 10 times starting right now d. No-par bond with the payoff Rp 50 million every year for five times, but starting in five years

Budi Frensidy - FEUI6 Valuation Case (2) e. Discretionary fund that gives cash Rp 12.5 million every year for the whole life starting next year f. Discretionary fund that gives cash Rp 11.5 million every year for the whole life starting next week g. Hedge fund with the payoff Rp 15 million every year for the whole life starting in three years h. Hedge fund that pays cash Rp 15 million next year, then becomes Rp 15.9 million the following year and steadily rises 6% every year, and the payments are for ten times only i. Banking product with the payoff Rp 13 million next week then Rp million next year and rises consistently 8% every year, and the payments are for ten times only j. Banking product that promises cash Rp 40 million in five years then becomes Rp 43.2 million a year after and steadily rises 8% every year, and the payments are for five times only

Budi Frensidy - FEUI7 Valuation Case (3) k. Investment trust that promises cash Rp 4 million next year, and then rises 8% every year for the whole life l. Investment trust that gives cash Rp 7 million next week, then Rp 7.35 million next year and rises on at 5% every year for the whole life m. Private equity with the payoff Rp 12 million starting in three years and rises to Rp million the following year and at 3% every year for the whole life n. Private equity that distributes cash Rp 12 million next year and rises Rp 60,000 every year for 50 years

Budi Frensidy - FEUI8 Valuation Case (4)  The security, risk, and certainty of the above financial assets are assumed the same. The investor is expected to act rationally and will base his decision only on the mathematical calculation. Using a different formula for each alternative, which asset should be chosen if the relevant discount rate is 12% p.a.?  To decide which asset should be chosen, the investor must calculate the present value of all the assets. As long as the present value of the cash flows generated from an asset is more than the cost which is Rp 100 million, the asset is worth buying  The problem is when there is a budget constraint, as we usually encounter, we have to rank all the choices and choose the highest value. This is what is meant by mutually exclusive projects in finance

Budi Frensidy - FEUI9 Equations and Results

Budi Frensidy - FEUI10 Equations and Results

Budi Frensidy - FEUI11 Summary  Based on the above results, the investor must choose asset d which is a no-par bond with the payoff Rp 50 million every year for five times, but starting in five years. This asset gives the highest present value namely Rp 114,545,022  Present value is the basics to understand financial management, investment management, and accounting  Certainly, there are some assumptions to be met in order for us to use the 13 equations. The amount of periodic cash flow must be equal, or they grow at an equal percentage or in equal difference from one period to another period. If one of these assumptions is fulfilled, the use of mathematical equations will give the same result as the present value derived from one by one calculation

Budi Frensidy - FEUI12 THANK YOU