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Benning Manufacturing Company is negotiating with a customer for the lease of a large machine manufactured by Benning. The machine has a cash price of $980,000. Benning wants to be reimbursed for financing the machine at a 9% annual interest rate. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.) Required: 1. Determine the required lease payment if the lease agreement calls for 10 equal annual payments beginning immediately. 2. Determine the required lease payment if the first of 10 annual payments will be made one year from the date of the agreement. 3. Determine the required lease payment if the first of 10 annual payments will be made immediately and Benning will be able to sell the machine to another customer for $68,000 at the end of the 10-year lease.

Respuesta :

TomShelby

Answer:

beginning inmediately:  $ 140,095.127

after a year:                    $ 152,703.688

with a salvage value:     $ 148,227.912

Explanation:

We need to find the PMT of 980,000 dollars being ordinary annuity or annuity-due discounted at 9%

Annuity-due:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate}(1+r) = C\\[/tex]

PV  $980,000.00

time 10

rate 0.09

[tex]980000 \div \frac{1-(1+0.09)^{-10} }{0.09} (1.09)= C\\[/tex]

C  $ 140,095.127

Annuity:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV  $980,000.00

time 10

rate 0.09

[tex]980000 \div \frac{1-(1+0.09)^{-10} }{0.09} = C\\[/tex]

C  $ 152,703.688

If there is a salvage value, we discounted from the lease value:

980,000 - present value of salvage value:

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]  

Maturity  $68,000.0000

time   10.00

rate  0.09

[tex]\frac{68000}{(1 + 0.09)^{10} } = PV[/tex]  

PV   28,723.93

980,000 - 28,724 = 951,276

Now we calculate the PMT:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV  $951,276.00

time 10

rate 0.09

[tex]951276 \div \frac{1-(1+0.09)^{-10} }{0.09} = C\\[/tex]

C  $ 148,227.912

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