1、1,Chapter 8 Compound Interest: future value and present value,8.6 Equivalent Payment Streams,2,We can compare the economic values of two payment streams.,First calculate the equivalent value of each stream at the same focal date.,Then compare the two equivalent values to rank them.,3,Criterion for t

2、he Equivalence of Two Payment Streams:,Two payment streams are equivalent if the sum of the equivalent values of the payments in one stream equals the sum of the equivalent values of the payments in the other stream, all evaluated at the same focal date.,4,Example,A financial obligation was to be se

3、ttled by a payment of $1500 on a date 1 year ago and a second payment of $2500 on a date 4 years after the first payment. The debtor missed the first payment and now wishes to pay $1000 today and to make two more payments in 11/2 and 3 years. The payment due in 3 years is to be twice as large as the

4、 payment due in 11/2 years. What should these payments be if the creditor can earn 8% compounded semiannually on any payment received?,5,Solution:,-1,11/2,0,1,2,3,year,Scheduled,-1,11/2,0,1,2,3,year,E2,E1,$2500,$1500,2x,$1000,x,E4,E3,new,6,E1= future value of $1500 on focal date E2= present value of

5、 $2500 on focal date E3= future value of $1000 on focal date E4= present value of 2x on focal date the equation of value is j=8% compounded semiannually m=2 i=j/m=4%,E1+ E2= E3+ E4,7,E1= future value of $1500 on focal date n=(1+11/2)*2=5,PV,PMT,n,1/y,FV,-1824.98,4,5,0,15,000,CPT,E2= present value of

6、 $2500 on focal date n=(3- 11/2)*2=3,FV,n,PV,2500,3,-2222.49,CPT,8,E3= future value of $1000 on focal date n= 11/2 *2=3,FV,PV,1000,-1124.86,CPT,E4= present value of 2x on focal date n=(3- 11/2)*2=3,FV,PV,2,-1.777993,CPT,E1+ E2= E3+ E4 x=$1052.06 2x=$2104.12,9,Example,One year ago Greg borrowed $5000

7、 from Cheray and agreed to repay the loan with two payments, 3 and 5 years after the date of the loan. Each payment is to consist of a principal portion of $2500 plus interest on that $2500 at 8% compounded quarterly from the date of the agreement. Greg now wishes to settle the debt by making two eq

8、ual payments, one in 6 months and the other in 2 1/2 years. What size of payments will put Cheray in an equivalent financial position if money now earns 7% compounded semiannually?,10,Solution:,-1,0,1,2,3,year,4,$2500,$2500,Payment 1,Payment 2,8% compounded quarterly,4,3,2,1,0,-1,2 1/2,1/2,x,x,Repla

9、cement stream,scheduled stream,7% compounded semiannually,11,Payment 1=the future value of a principal portion of $2500 at 8% compounded quarterly 3 years after the date of the loan j=8% m=4 i=2% n=3*4=12 p=$2500,PV,PMT,n,1/Y,FV,-3170.60,2,12,0,2500,CPT,12,Payment 2=the future value of a principal p

10、ortion of $2500 at 8% compounded quarterly 5 years after the date of the loan j=8% m=4 i=2% n=5*4=20 p=$2500,n,FV,20,-3714.87,CPT,13,4,3,2,1,0,-1,2 1/2,1/2,x,x,4,3,2,1,0,-1,1/2,E1,$3170.60,E2,$3714.87,year,year,E3,E1+ E2= E3+ x,14,E1= the present value of payment 1 ($3170.60) j=7% compounded semiannually m=2 i=j/m=3.5%,PV,PMT,n,1/y,FV,-2859.70,3.5,3,0,3170.60,CPT,15,E2= the present value of payment 2 ($3174.87) i=j/m=3.5%,FV,n,PV,3174.87,7,-2919.85,CPT,16,E3= the present value of x made in years i=j/m=3.5%,FV,n,PV,1,4,-0