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1、1,Chapter 7 Applications of Simple Interest,7.2 Valuation Principle,2,Example: an investment that will deliver a single payment of $110 in 1 year. What is the most you should pay to buy the investment if you require a minimum rate of return of 10% pa? Or you require a rate of return of 8% pa?,Soluti
2、on:,3,The process of calculating a payments present value is often called “discounting the payment”.The interest rate used in the present value calculation is then often called the discount rate.,4,For investments purchased privately, you have some flexibility to negotiate a higher rate of return by
3、 bargaining down the price. But for various types of investments available to the general public, the rates of return are determined by market forces of supply and demand.,5,When an investments price is established by competitive bidding among many buyers and sellers, we refer to the price as the fa
4、ir market value.,6,A particular fair market value implies a specific value for the rate of return used to discount the future cash flows from the investment. This rate of return is what we mean by the market-determined rate of return.,7,For publicly traded investments, you only decision is whether t
5、o accept or reject the prevailing price and market-determined rate of return.,8,These ideas are so important and of such wide application in finance that they are formally embodied in Valuation Principle.,9,Valuation Principle,The fair market value of an investment is the sum of the present valuesof
6、 the expected cash flows.,The discount rate used in the present-valuecalculations should be the market-based rate of return required for this type of investment.,10,The Valuation Principle is an extension of the concept of the equivalent value of a payment stream. The sum of present values of the ex
7、pected cash flows represents their combined equivalent value on the investment date. The time value of money in this context is the market-based required rate of return.,11,Example 7.2 A Valuation of a Non-Interest-Bearing Obligation,An investment contract calls for a payment of $1000 five months fr
8、om now and another payment, 10 months from now, of $1500.a,What price will an investor be prepared to pay for the investment today if the required rate of return is 12% pa?b,Demonstrate that the investor will realize a 12% rate of return on the purchase price if the payments are received as expected
9、.,12,months,0,5,10,today,$1000,$1500,P1,P2,sum,Solution:,13,a,P1 represents the present value of $1000 in 5 months r1=12% t1=5/12 years s1=$1000,14,P2 represents the present value of $1500 in 10 months An investor requiring a 12% rate of return should be willing to pay $2316.02 today for the contrac
10、t.,15,b,Demonstrate that the investor will realize a 12% rate of return on $952.38 and $1363.64 respectively.$952.38 will grow to $1000 in 5 months at 12% Similarly, it can be shown that $1500 payment received after 10 months returns the $1363.64 component of the initial investment plus 10 months in
11、terest on $1363.64 at 12%.,16,Example 7.2 B Valuation Of An Interest-Earning Obligation,On March 1 Murray signed a contract to pay Anton or his designate $2000 plus interest at 8% pa on June 1, and $3000 plus interest at 8% pa on September 1. Anton sold the contract on May 1 at a price that will yie
12、ld the buyer a 10% rate of return. What was the price?,17,March 1,May 1,June 1,September 1,P1=$2000,P2=$3000,S1,E1,S2,E2,r1=8%,r2=8%,r=10%,r=10%,Solution:,18,step 1:calculate the future value of $2000 p1=$2000 s1=future value value of $2000.The exact number of days from March 1 to June 1 is t1=(31-1
13、+1)+30+31+(1-1)=92 days s1=p1(1+r1t1),19,Step 2:calculate the future value of $3000 the exact number of days from March 1 to September is t2=(31-1+1)+30+31+30+31+31+(1-1)=184 days p2=$3000 r2=8% t2=184/365 s2=p2(1+r2t2),20,Step 3: calculate the present value E1 of s1 on May 1.the exact number of day
14、s from May1 to June 1 is t3=(31-1+1)+(1-1)=31 days r=10%,21,Step 4:calculate the present value E2 of s2 on May 1.the exact number of days from May1 to September 1 is t4=(31-1+1)+30+31+31+(1-1)=123days r=10%,22,Step 5: the price is the sum of E1and E2price=E1+E2=$5042.40the buyer paid $5042.40 for the contract.,23,Exercise:P-252: 5,6P-257: 3,5P-242: 11,13P-238: 7,Assignment 1:P-245: all review problems of chapter 6,
