Simplifying
(2a + 5)(3a + -4) = 0
Reorder the terms:
(5 + 2a)(3a + -4) = 0
Reorder the terms:
(5 + 2a)(-4 + 3a) = 0
Multiply (5 + 2a) * (-4 + 3a)
(5(-4 + 3a) + 2a * (-4 + 3a)) = 0
((-4 * 5 + 3a * 5) + 2a * (-4 + 3a)) = 0
((-20 + 15a) + 2a * (-4 + 3a)) = 0
(-20 + 15a + (-4 * 2a + 3a * 2a)) = 0
(-20 + 15a + (-8a + 6a2)) = 0
Combine like terms: 15a + -8a = 7a
(-20 + 7a + 6a2) = 0
Solving
-20 + 7a + 6a2 = 0
Solving for variable 'a'.
Factor a trinomial.
(-5 + -2a)(4 + -3a) = 0
Subproblem 1
Set the factor '(-5 + -2a)' equal to zero and attempt to solve:
Simplifying
-5 + -2a = 0
Solving
-5 + -2a = 0
Move all terms containing a to the left, all other terms to the right.
Add '5' to each side of the equation.
-5 + 5 + -2a = 0 + 5
Combine like terms: -5 + 5 = 0
0 + -2a = 0 + 5
-2a = 0 + 5
Combine like terms: 0 + 5 = 5
-2a = 5
Divide each side by '-2'.
a = -2.5
Simplifying
a = -2.5
Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve:
Simplifying
4 + -3a = 0
Solving
4 + -3a = 0
Move all terms containing a to the left, all other terms to the right.
Add '-4' to each side of the equation.
4 + -4 + -3a = 0 + -4
Combine like terms: 4 + -4 = 0
0 + -3a = 0 + -4
-3a = 0 + -4
Combine like terms: 0 + -4 = -4
-3a = -4
Divide each side by '-3'.
a = 1.333333333
Simplifying
a = 1.333333333
Solution
a = {-2.5, 1.333333333}
Answer:
The cost of equity using the DCF method: 4.39%.
The cost of equity using the SML method: 15.01%.
Explanation:
a. The cost of equity using the DCF method:
We have: Current stock price = Next year dividend payment / ( Cost of equity - Growth rate) <=> Cost of equity = Next year dividend payment/Current stock price + Growth rate = 0.3 x 1.04/80 + 4% = 4.39%.
b. The cost of equity using the SML method:
Cost of equity = Risk free rate + beta x ( Market return - risk free rate); in which Risk free rate is rate on T-bill.
=> Cost of equity = 6.3% + 1.3 x ( 13% -6.3%) = 15.01%.
Answer:
Month incurred Amount June July August
June 75,000 37500 18,750 18,750
July 95,000 47,500 23,750
August 95,000 47,500
37,500 66,250 90,000
The expected cash receipts are:
June = $37,500
July = $66,250
August = $90,000
Explanation:
The pattern of collection of sales is that 50% are collected in the months of sales while 25% each will be collected in the following month and following 2 months. For instance, 50% of June sales are collected in June, 25% are realized in July and 25% are collected in August. 50% of July sales are realized in July and 25% are collected in August.
Answer:
$1905
Explanation:
Here we will have to calculate Economic Order Quantity to lower the ordering ordering and holding cost as much as we can. So here we will use the following formula to calculate the best number of units that we should order, which is as under:
Economic Order Quantity = SquareRoot (2 * Annual Demand * ordering cost per order / Holding cost per unit per year)
Here
Annual Demand = 900kg of palm oil per day * 52 weeks * 5 day a week / 7
Annual Demand = 900 * 52 * 5 / 7 = 33,429
And
Ordering cost per order = $57 per order
Annual holding cost per unit per year is 20% of $5.25 per kg which is $1.05.
So by putting values, we have:
Economic Order Quantity = Square Root (2 * 33,429 * 57 / 1.05)
Economic Order Quantity = 1905 kgs
Answer:
$1,088.12
Explanation:
The formula for calculating monthly repayments is as below.
M= P x <u> r </u>
1 − (1+r)−^n
where p is the loan amount = $220,000
r = 4.3per cent or 0.043 % interest rate per year,
on monthly basis r will be 0.043/12=0.00358%
n = 30 year, which is 30 x 12 months= 360 months
M= $220,000 x <u> 0.00358 </u>
1 - (1+0.00358 ) ^ - 360
M=$220,000 x<u> 0.00358 </u>
1- 0.2762
M = $220,000 x (0.00358 /0.7238)
M = $220,000 x 0.0049461
M = 1,088.12
Monthly payments will be $1,088.12
