Answer to Question #188257 in Financial Math for Inara Shah

Question

        Question 2

After these previous calculations, the project still requires a big initial investment, and other options are being considered. We were considering adapting our production line, in order to produce some parts for electric automobiles, this way, and after analyzing the possible market opportunities, we could expect to obtain net revenues of $40,000 per month for at least the next 8 years. 

 

a)     What is the maximum that we should invest on this project if we consider a cost of capital of 4%?

 

b)     If we ask for a loan of 2,000,000 at an annual interest rate of 2% compounded semiannually, to be paid in 8 years, how much would you have to pay every semester to cover the loan?

 

 

 (25%)

 

 

 

 

Answer 1

(a)

Monthly revenue(P)=40000

WACC=4%

monthly WACC(r)=4%/12=0.33333333%=0.0033333333

years=8

Terms(n0=8*12=36

Amount that should be paid today$=P\times\frac{[1-\frac{1}{(1+r)^n}]}{r}$

$=40000\times\frac{[1-\frac{1}{(1+0.0033333333)^{96}}]}{0.0033333333}$

$=40000\times \frac{1-0.726535563}{0.0033333333}$

$=40000\times \frac{0.273464436}{0.0033333333}$

$=40000\times 82.03933185$

$=3,281,573.274$

The amount that should be paid for the inflow of 40000 is $\$3,281,573.274$

(b)

Amount of Loan = 2,000,000

Interest Rate(r) = 2% Compounded semi annully = 2%/2 =1% per semester = 0.01

Years = 8 

Terms(n) = 8*2 =16

Let Semiannual payment =P

$P\times \frac{[1-\frac{1}{(1+r)^n}]}{r}=2,000,000$

$P\times \frac{[1-\frac{1}{(1+0.01)^{16}}]}{0.01}=2,000,000$

$P\times \frac{1-0.852821262}{0.01}=2000000$

$P\times \frac{0.147178737}{0.01}=2000000$

$P\times 14.71787378=2000000$

$P=\frac{2000000}{14.71787378}$

$P=135889.1936$

Semi annual payments $=\$135,889.1936$