Question

a)An investment pays $10,000 after 1 year and it pays another $8,000 after another 1 year. The interest rate is 5%. What is the present value of this investment?

b)A bond's face value is the amount the issuer provides to the bondholder, once maturity is reached. A bond's face value is $100,000 and it mature after five years. If the interest rate is 1.5%, how much would you pay (at most) to purchase this bond?

Answer 1

An investment pays $10,000 after 1 year and it pays another $8,000 after another 1 year. The interest rate is 5%. What is the present value of this investment?

Present Value

= Summation of Discounted value of the amount paid out at the end of each year

= > Present value (PV)

= payment after 1 year discounted at today’s value by market rate of interest + payment after two years discounted at today’s value

= > PV = 10000/(1+0.05)    + 8000/(1+0.05)2

            = 10000/1.05 + 8000/(1.05)2

              = 16780.05

b)A bond's face value is the amount the issuer provides to the bondholder, once maturity is reached. A bond's face value is $100,000 and it mature after five years. If the interest rate is 1.5%, how much would you pay (at most) to purchase this bond?

Its only viable to buy the bond when Bond’s purchase value today is less than or equal to (at max) the present discounted value (at the prevailing market interest rate ) of its face value paid out on maturity .

= > Bond’s at max purchase value = 100000/(1+0.015)5

                                                                        = 92826.03