Question

A construction manager just starting in private practice needs a van to carry crew and equipment. She can lease a used van for $3,576 per year, paid at the beginning of each year, in which case maintenance is provied. Alternatively, she can buy a used van for $6,461 and pay for maintenance herself. She expects to keep the van for three years at which time she could sell it for $1,437. What is the most she should pay for uniform annual maintenance to make it worthwhile to buy the van instead of leasing it, if her MARR is 20%

Answer 1

Answer:

The answer is "1832".

Explanation:

The PVAF(r,n) start value$= \frac{(1+r)^{n-1} -1 \ \ +1}{r \times (1+r)^n-1}$

The PVAF(r,n) end value$= \frac{(1+r)^{n} -1}{r \times (1+r)^n}$

The PVF(r,n)  value $= \frac{1}{(1+r)^n}$

$r = \text{Rate of dirscount} \\\\n = terms$

$\text{Present Value= Monthly rent} \times PVAF$

PVAF(20%, 3) starting = 2.5278

PVAF(20%, 3) ending = 2.1065

PVAF(20%, 3) starting = 5787

calculating the lease payment of present value:

$present \ value = Lease\ payment \times PVAF(10 \%,3) starting$

                      $=3609 \times 2.5278\\\\=9122.75$

existing importance by busing excluding annual servicing

$\text{present value = cost - sale value} \times PVF(20 \%,3)$

                     $=6113-1469\times 0.5787 \\\\=5262.88$

Calculating the annual maintanance=$\frac{\text{present value of leasing -buying}}{ PVAF(20 \%,3) ending}$

                                                            $=\frac{3859.87}{2.1065}\\\\=1832.32 \ \ \ or \ \ \ 1832$