Question

I am considering selling my current home through an owner financed arrangement. I have been
offered $1,000 per month for 20 years with the first payment due immediately plus an
additional $100,000 with the last payment at the end of 20 years. If the appropriate discount
rate is 6% APR compounded monthly, then what is the equivalent cash offer for my house?

Answer 1

Equivalent Cash offer = PV of CFs

PV of Annuity Due of $ 1000 per month :

PV of Annuity Due:

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here cash flows are happened at the begining of the period. PV of annuity is current value of cash flows to be received at regular intervals discounted at specified int rate or discount rate to current date.

PV of Annuity Due = Cash Flow + [ Cash Flow * [ 1 - [(1+r)^-(n-1)]] /r ]
r - Int rate per period
n - No. of periods

Particulars	Amount
Cash Flow	$            1,000.00
Int Rate	0.500%
Periods	240

PV of Annuity Due = [ Cash Flow + Cash Flow * [ 1 - [(1+r)^-(n-1)]] / r ]
= [ $ 1000 + $ 1000 * [ 1 - [(1+0.005)^-239] ] / 0.005 ]
= [ $ 1000 + $ 1000 * [ 1 - [(1.005)^-239] ] / 0.005 ]
= [ $ 1000 + $ 1000 * [ 1 - [0.3036] ] / 0.005 ]
= [ $ 1000 + $ 1000 * [0.6964] ] / 0.005 ]
= [ $ 1000 + $ 139278.68 ]
= $ 140278.68
PV of $ 100000 after 20 Years:

Present Value:

Present value is current value of Future cash flows discounted at specified discount Rate.

PV = FV / (1+r)^n
Where r is Int rate per period
n - No. of periods

Particulars	Amount
Future Value	$          100,000.00
Int Rate	0.5000%
Periods	240

Present Value = Future Value / ( 1 + r )^n
= $ 100000 / ( 1 + 0.005 ) ^ 240
= $ 100000 / ( 1.005 ) ^ 240
= $ 100000 / 3.3102
= $ 30209.61

Cash offer Price = $ 140278.68 + $ 30209.61

= $ 170488.29