Question

Environmental recovery company RexChem Part- ners plans to finance a site reclamation project that will require a 4-year cleanup period. The company plans to borrow $1.8 million now. How much will the company reveice in annual paymebts

Answer 1

Complete question Text:

Environmental recovery company RexChem Partners plans to finance a site reclamation project that will require a 4-year cleanup period. The company will borrow $1.8 million now to finance the project. How much will the company have to receive in annual payments for 4 years, provided it will also receive a final lump sum payment after 4 years in the amount of $800,000? The MARR is 10% per year on its investment

Answer:

We are going to receive annual payment of $395,471

Explanation:

We solve for the present value of the lump-sum today:

PRESENT VALUE OF LUMP SUM

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  800,000.00

time   4.00

rate  0.1

$\frac{800000}{(1 + 0.1)^{4} } = PV$  

PV   546,410.76

Now, we deduct this fromthe 1,800,000 loan:

1,800,000 - 546,410.76 = 1,253,589.24

this value will be the amount the yearly installment will ghave to pay.

Installment of a present annuity

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  1,253,589.24 €

time 4

rate 0.1

$1253589.24 \div \frac{1-(1+0.1)^{-4} }{0.1} = C$

C  $ 395,470.805