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1. Finding Present Values:

What is the present value of the following future payments:

a) $1,210 in 2 years at a 10% discount rate:

present value = $1,210!1"10)2

= $1000

#) $1,2"&1 in ' years at an (% discount rate: present value = $1,2"&1!1"0()' = $1000

c) $1,00 in 1 year at a % discount rate: present value = $1,00!1"0)1= $1000

2. General formula for finding the present value of several future annual payments

Present Value = P1/(1+r1

+ P2/(1+r2

+ +(F + Pn/(1+rn

!here 1" 2" n = num#er of years$ r = dis%ount rate$ Pn= payment$ F = fa%e value

&. Finding Present Values 'sing the General Formula:

a) *ou can ma+e two different investments" he interest you receive on the firstinvestment is $110 per year for three years" *ou receive $''0 on the secondinvestment in the third year and nothing in the first two years" -f your discount rate is.%, what should you pay for each of these investments/

resent alue of 1 = $110 3 $110 3 $110 = $2"0' !1"0.) !1"0.)2 !1"0.)'

resent alue of 2 = $0 3 $0 3 $''0 = $ 2&&"0& !1"0.) !1"0.)2 !1"0.)'

ou )ill pay more for investment *1

#) *ou can ma+e two different new products at your plant" roduct 1 is e4pected toearn no profit in the first year, $00 in the second year and $1,000 in the third year"roduct 2 is e4pected to earn $00 per year for three years" 5ssume your cost of

capital is 10%" Which product should you ma+e/

resent alue of 1 = $0 3 $00 3 $1000 = $ 1,1."' !1"10) !1"10)2 !1"10)'

resent alue of 2 = $00 3 $00 3 $00 = $1,2'"' !1"10) !1"10)2 !1"10)'he present value of future profits is higher for produ%t *2 "

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c) 5ssume you have a winning lottery tic+et and the state offers you $,000 now orpayments of $2,000 for three years" -f your discount rate is 10%, which alternativeshould you choose/

resent alue = $2000 3 $2000 3 $2000 = $,&'"&0 !1"10) !1"10)2 !1"10)'

,hoose a lump sum payment of -".

0. Finding ond Pri%es 'sing the General Formula:

a) 6ind the value of a note with a remaining term of three years, a face value of $10,000and a coupon of $00 per year" 5ssume the mar+et yield is %"

alue = $00 3 $00 3 $10,00 = $10,2&&"21 !1"0)1 !1"0)2 !1"0)'

#) 6ind the value of a note with a remaining term of three years, a face value of $10,000and a coupon of $00 per year" 5ssume the mar+et yield is now .%"

alue = $00 3 $00 3 $10,00 = $,&'2"(2 !1"0.)1 !1"0.)2 !1"0.)'

ond pri%es move inversely )ith interest rates. hey %an #e ea%tly determined as

interest rates %hange.