Chapter 6 Concept Videos

Present and future value tables of $1 at 11% are presented below. Lorien, Inc. leased tree excavators under terms of $10,000 down and four equal annual payments of $30,000 on the anniversary date of the lease. The interest rate implicit in the lease is 11%. For what amount would Lorien initially record the asset and lease liability?

$103,074 Present Value of an Ordinary Annuity = $30,000 × 3.10245* = $93,074 Add the $10,000 down payment already at present value: $93,074 + $10,000 = $103,074 *PVA: n = 4; i = 11%

What is the present value of $6,000 to be received at the end of each of eight periods, assuming the first payment occurs at the end of the fourth year and an interest rate of 10%? (Refer to the appropriate table in the Present and Future Value Tables section of your text.)

$24,049 Calculate the present value of the ordinary annuity: PVA (i=10%, n=8) = $6,000 × 5.33493 = $32,010. This is the present value of the annuity as of the beginning of the fourth year. Calculate the present value of the amount in Step 1.: PV (i=10%, n=3) = $32,010 × 0.75131 = $24,049. This is the present value of the amount in Step 1 from the beginning of the fourth year to the beginning of the first year (today).

What is the present value of $5,000 to be received five years from now, assuming an interest rate of 8%? (Refer to the appropriate table in the Present and Future Value Tables section of your text.)

$3,402.90 Following the 8% interest rate column down to the fifth period gives the present value factor of 0.68058. Multiply the $5,000 future value times the present value factor of 0.68058 to get $3,402.90. Remember, the present value will always be less that the future value because of interest.

What is the present value of $6,000 to be paid at the end of each of the next eight periods assuming an interest rate of 10%? (Refer to the appropriate table in the Present and Future Value Tables section of your text.)

$32,010 An annuity is a series of equal payments. If the payments come at the end of each period, they represent an ordinary annuity. We use the present value of an annuity (PVA) table for ordinary annuities. Multiply the payment of $6,000 per period times the present value of an ordinary annuity interest factor in the 10% column and the eighth row: $6,000 × 5.33493 = $32,010.

What is the present value of $6,000 to be paid at the beginning of each of the next eight periods assuming an interest rate of 10%? (Refer to the appropriate table in the Present and Future Value Tables section of your text.)

$35,211 An annuity is a series of equal payments. If the payments come at the beginning of each period, they represent an annuity due. We use the present value of an annuity due (PVAD) table for annuities due. Multiply the payment of $6,000 per period times the present value of an annuity due interest factor in the 10% column and the eighth row: $6,000 × 5.86842 = $35,211.

Mufala, Inc., will issue $10,000,000 of 6% 10-year bonds. The market rate for bonds with similar risk and maturity is 8%. Interest will be paid by Mufala semiannually. What is the issue price of the bonds? (Refer to the appropriate table in the Present and Future Value Tables section of your text. (Round your answer to the nearest whole dollar.)

8,640,999 Interest payment = $10,000,000 × 3% (6% ÷ two semi-annual payments) = $300,000 n = 20 (10 years × two semiannual payments); i = 4% (8% market rate ÷ 2 semiannual payments) PVA = $300,000 × 13.59033 (n=20, i=4%) = $4,077,099 PV of the $10,000,000 face amount that will be received in 10 years: n = 20 (10 years × two semiannual payments); i = 4% (8% market rate ÷ 2 semiannual payments) PV = $10,000,000 × 0.45639 (n=20, i=4%) = $4,563,900 $4,077,099 + $4,563,900 = $8,640,999

If you borrow $30,000 from the bank for 5 years (60 months) at 12% interest, you would calculate the payment required at the end of each month by:

Dividing $30,000 by the present value of an ordinary annuity of $1, where i = 1% and n=60.

The City of Smithfield's pension fund is projecting the amount necessary today to fund an employee's pension benefits. The employee has worked for the city for 10 years and will retire in 30 years from now. Retirement payments are expected to last for a total of 20 years and payments will be made to the employee at the end of each retirement year. Which of the following best describes the computation of the amount needed at the end of year 10 to fund the retiree's annuity due to her 10 years of service to date?

Present value of $1 for 30 periods, times the present value of an ordinary annuity of 20 payments, times the annual annuity payment.