Question

Consider a bond that pays a $500 dividend once a quarter.

It pays in the months of March, June, September, and December.

It promises to do so for 10 years after you purchase it (start in January 2019).

You discount the future at rate r=0.005r=0.005 per month.

a. How much do you value the asset in January 2019?

b. Consider a different asset that pays a lump sum at its expiration date rather than a quarterly dividend of $500 dollars, how much would this asset need to pay in December 2028 (the final payment date of the quarterly asset) for the two assets to be equally valued?

c. How much should you be willing to pay if your friend bought the quarterly asset (from the main text) in January 2019 but wanted to sell it to you in October 2019?

Answer 1

a.

When there are number of constant payments at constant intervals , it is called annuity.

To find the present value of number of fixed payment at constant interval , you use

Uniform Series Present Worth Factor=PWF=(P/A,i,N)=(((1+i)^N)-1)/(i*((1+i)^N))

Multiply this factor by the constant periodic payment of A, you will get the Present Value (PV)

Discount rate per month=0.005

Discount rate per quarter=((1+0.005)^3)-1=0.01508=1.508%

i=discount rate per quarter=1.508%=0.01508, N=Number of payments=4*10=40

PVF=(((1+i)^N)-1)/(i*((1+i)^N))=(((1+0.01508)^40)-1)/(0.01508*((1+0.01508)^40))=29.8722

VALUE OF ASSET IN JANUARY 2019=$500*29.8722=$14,936

b

There is a Single Payment at future

Single Payment Future Worth Factor (F/P, i,N)=((1+i)^N)

i=Interest rate, N=Number of Years after which the Single Payment is made

Number of Months to future =10*12=120

i=Monthly discount rate =0.005

N=120

Future Value =$14936*((1+i)^N)=14936*((1+0.005)^120)=$27,175

The asset need to pay in December 2028=$27,175

c.

If it is sold in October 2019

i=0.005

N=Number of months=9(January to October)

Future Value=$14936*(1.005^9)=$15,622

Amount willing to pay=$15,622