Fair Value of Money Calculation

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1.) On January 1, 2010, Ott Co. sold goods to Flynn Company. Flynn signed a zero-interest-bearing note requiring payment of $80,000 annually for seven years. The first payment was made on January 1, 2010. The prevailing rate of interest for this type of note at date of issuance was 10%. Ott should record sales revenue in January 2010 of what?

Present value of annuity due
PVad = [ $80,000 x f( n=7, i=10%)] x (1+.10)
PVad = $80,000 x 4.868 x 1.10 = $428,384

2.) On January 1, 2010, Haley co. issued ten-year bonds with a face amount of $2,000,000 and a stated interest rate of 8% payable annually on January 1. The bonds were priced to yield 10%. What was the total price of the bonds?

Requires both Present value of a single sum and ordinary annuity

PVss = $2,000,000 x f( n=10, i=10%)
PVss = $2,000,000 x .386 = $772,000

PVa = ($2,000,000 x .08) x f( n=10, i= 10%)
PVa = $160,000 x 6.145 = $983,200

Price of bonds = $772,000 + $983,200 = $1,755,200

3.) Jeremy Leasing purchases and then leases small aircrafts to interested parties. The company is currently determining the required rental for a small aircraft that cost them $400,000. If the lease if for eight years and annual lease payments are required to be made at the end of each year, what will be the annual rental if Jeremy wants to earn a return of 10%?

Use the present value for an ordinary annuity formulas to find the rent value

PVa = Rent x f( n=8, i=10%)
$400,000 = Rent x 5.335
$400,0005.335 = Rent = $74,977
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