1.John wants to make a deposit on 1/1/2016 to be able to withdraw $1,000 at the
ID: 2423093 • Letter: 1
Question
1.John wants to make a deposit on 1/1/2016 to be able to withdraw $1,000 at the beginning of each year starting 1/1/2020 for four years. The interest rate is 6 percent.
2.Timken Company issues a $1,000,000 bond at 9% for 10 years. The market interest rate is 10%.
Required:
1. What is the issue price of these bonds and the bond discount or premium?
2. Assume that Timken uses the effective interest method to amortize the bond discount or premium for the annual interest payments, what is the interest expense and the amount of cash paid on the first interest payment?
Explanation / Answer
Q1 --- John wants to make a deposit on 1/1/2016 to be able to withdraw $1,000 at the beginning of each year starting 1/1/2020 for four years. The interest rate is 6 percent.
Answer
First we need to calculate the Value of amount as on 1/1/2020 which Mr. John will get each year starting from 1/1/2020 for four years. The expected inflow Mr. John want to get each year is shown in the below table:
Date
Value
1/1/2020
$1,000
1/1/2021
$1,000
1/1/2022
$1,000
1/1/2023
$1,000
Since the inflow of equal amount is at the beginning of year, it is Annuity Due where the inflow/outflow occurs at the beginning of each period.
PV of Annuity Due on 1/1/2020 = Amount x PVIFA (6%, 4)
We can calculated PVIFA (6%, 4) by using following formula = [ 1 – 1/(1+R)n] / R x (1 + R)
Here R = Rate of Interest = 6% p.a.
N = no of year = times = 4
So, the value of PVIFA (6%, 4) = [ 1 – 1/(1+0.06)4 ] / 0.06 x (1+0.06) = 3.673
PV of Annuity Due on 1/1/2020 = $1,000 x 3.673 = $3,673
So the future value of amount to be deposited today must be $3,673 on 1/1/2020 in order to get $1,000 each at the beginning of year from 1/1/2020 for 4 year i.e. upto 1/1/2023.
We need to find out Present Value of $3,673 as on today.
The amount to be deposited today = Value of Amount on 1/1/2020 x PVIF (6%, 4) = $3,673 x 1/(1+0.06)4 = $3,673 x 0.792 = $2,909 or $2,910
Therefore, Mr. John must deposit $2,910 today to get $1000 each at the beginning of year from 1/1/2000 for 4 years.
Q2 -- Timken Company issues a $1,000,000 bond at 9% for 10 years. The market interest rate is 10%.
Required:
1. What is the issue price of these bonds and the bond discount or premium?
2. Assume that Timken uses the effective interest method to amortize the bond discount or premium for the annual interest payments, what is the interest expense and the amount of cash paid on the first interest payment?
Answer:
(i)
Issue Price is the current value of bond.
Present Value of Bond = Interest x PVIFA (Market Rate, Years) + Maturity Value of Bond x PVIF (Market Rate, Time) --------------------- equation 1
Here,
Time (n) = 10 years
Interest Amount = $1,000,000 x 9% = $90,000 (Interest amount is always calculated on face value and by taking coupon rate of bond).
Market Interest Rate ( R) = 10%
Value of PVIFA (10%, 10) = [ 1 – 1/(1+R)n] / R = [1 – 1/(1+0.10)10] / 0.10 = 6.144567106 or 6.145
Value of PVIF (10%, 10) = 1/(1+0.10)10 = 0.3855432894 or 0.3855
By putting this value in equation 1, we get:
Present Value of Bond (Issue Price) = ($90,000 x 6.145) + ($1,000,000 x 0.3855) = $553050 + $385,500 = $938,650
Bond are selling at discount of $61,450 i.e. Face Value of Bond - Issue Price = $1,000,000 - $938,650 = $61,450
(2)
Amount of each amortization of Discount on Bond = Discount on Bond/No of years = $61,450 / 10 = $6,145
Cash Interest to be paid to Bond Holders = $1,000,000 x 9% = $90,000
Discount on Bond to be amortized first year = $6,145
Total Interest Expenses = Cash Interest + Amortization on Discount of Bond = $90,000 + $6,145 = $96,145
Date
Value
1/1/2020
$1,000
1/1/2021
$1,000
1/1/2022
$1,000
1/1/2023
$1,000
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