Answer:
The cross-over point is about 22 computers.
Explanation:
Fixed cost, F = 0
Variable cost = $50
Option B
Fixed cost, F = $1,000
Variable cost, V = $5
Therefore,
Total cost = F + (n × V)
n = no of units
Option A
Total cost TC = 50n
Option B
Total cost TC = 1000 + 5n
We can calculate cross-over point by equalizing two options
:
50n = 1000 + 5n
45n = 1000
n = 22.2
The cross-over point is about 22 computers.
Answer:
A. 7.95%.
Explanation:
Calculate the expected rate of return for the investment as follows:
![\begin{aligned}\text { Expected rate of return } &=(\text { Probability } \times \text { Rate of return })+(\text { Probability } \times \text { Rate of return })+\\&(\text { Probability } \times \text { Rate of retum }) \\=&(0.40 \times 15 \%)+(0.50 \times 10 \%)+(0.10 \times-3 \%) \\=& 0.06+0.05-0.003 \\=& 0.107](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%3C%2Fp%3E%3Cp%3E%5Ctext%20%7B%20Expected%20rate%20of%20return%20%7D%20%26%3D%28%5Ctext%20%7B%20Probability%20%7D%20%5Ctimes%20%5Ctext%20%7B%20Rate%20of%20return%20%7D%29%2B%28%5Ctext%20%7B%20Probability%20%7D%20%5Ctimes%20%5Ctext%20%7B%20Rate%20of%20return%20%7D%29%2B%5C%5C%3C%2Fp%3E%3Cp%3E%26%28%5Ctext%20%7B%20Probability%20%7D%20%5Ctimes%20%5Ctext%20%7B%20Rate%20of%20retum%20%7D%29%20%5C%5C%3C%2Fp%3E%3Cp%3E%3D%26%280.40%20%5Ctimes%2015%20%5C%25%29%2B%280.50%20%5Ctimes%2010%20%5C%25%29%2B%280.10%20%5Ctimes-3%20%5C%25%29%20%5C%5C%3C%2Fp%3E%3Cp%3E%3D%26%200.06%2B0.05-0.003%20%5C%5C%3C%2Fp%3E%3Cp%3E%3D%26%200.107)
Calculate the standard deviation of the investment as follows:
![\begin{aligned}\text { Standard deviation }=&\left\{\begin{array}{l} \text { Probability } \left.\times(\text { Return }-\text { Expected return })^{2}\right)+ \\\text { (Probability } \left.\times(\text { Return }-\text { Expected return })^{2}\right)+ \\\text { (Probability } \left.\times(\text { Return }-\text { Expected return })^{2}\right)\end{array}\right.](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%3C%2Fp%3E%3Cp%3E%5Ctext%20%7B%20Standard%20deviation%20%7D%3D%26%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bl%7D%20%3C%2Fp%3E%3Cp%3E%5Ctext%20%7B%20Probability%20%7D%20%5Cleft.%5Ctimes%28%5Ctext%20%7B%20Return%20%7D-%5Ctext%20%7B%20Expected%20return%20%7D%29%5E%7B2%7D%5Cright%29%2B%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctext%20%7B%20%28Probability%20%7D%20%5Cleft.%5Ctimes%28%5Ctext%20%7B%20Return%20%7D-%5Ctext%20%7B%20Expected%20return%20%7D%29%5E%7B2%7D%5Cright%29%2B%20%5C%5C%3C%2Fp%3E%3Cp%3E%5Ctext%20%7B%20%28Probability%20%7D%20%5Cleft.%5Ctimes%28%5Ctext%20%7B%20Return%20%7D-%5Ctext%20%7B%20Expected%20return%20%7D%29%5E%7B2%7D%5Cright%29%3C%2Fp%3E%3Cp%3E%5Cend%7Barray%7D%5Cright.)
=![\sqrt{\left(0.40 \times(0.15-0.107)^{2}\right)+\left(0.50 \times(0.10-0.107)^{2}\right)+} \\=\sqrt{0.0007396+0.0000245+0.0018769} \\=\sqrt{0.002641} \\=0.05139066063011](https://tex.z-dn.net/?f=%5Csqrt%7B%5Cleft%280.40%20%5Ctimes%280.15-0.107%29%5E%7B2%7D%5Cright%29%2B%5Cleft%280.50%20%5Ctimes%280.10-0.107%29%5E%7B2%7D%5Cright%29%2B%7D%20%5C%5C%3C%2Fp%3E%3Cp%3E%3D%5Csqrt%7B0.0007396%2B0.0000245%2B0.0018769%7D%20%5C%5C%3C%2Fp%3E%3Cp%3E%3D%5Csqrt%7B0.002641%7D%20%5C%5C%3C%2Fp%3E%3Cp%3E%3D0.05139066063011)
Answer:
It will take 10 years to have $20,000 on investment of $10,000.
Explanation:
Annual Rate of return = r = 7%
Compounded Value / Future Value = FV = $20,000
Investment Value / Present Value = PV = $10,000
Use Future value formula to solve this question:
Future Value = Present Value x ( 1 + Number of Year )^Number of year
FV = PV x ![( 1 + r )^{n}](https://tex.z-dn.net/?f=%28%201%20%2B%20r%20%29%5E%7Bn%7D)
$20,000 = $10,000 x ![( 1 + 0.07 )^{n}](https://tex.z-dn.net/?f=%28%201%20%2B%200.07%20%29%5E%7Bn%7D)
= ![( 1 + 0.07 )^{n}](https://tex.z-dn.net/?f=%28%201%20%2B%200.07%20%29%5E%7Bn%7D)
$2 = ![1 .07 ^{n](https://tex.z-dn.net/?f=1%20.07%20%5E%7Bn)
Log 2 = n log 1.07
0.30 = n x 0.03
n = ![\frac{0.30}{0.03}](https://tex.z-dn.net/?f=%5Cfrac%7B0.30%7D%7B0.03%7D)
n = 10.00
n = 10 year (rounded off to nearest year )
It will take 10 years to have $20,000 on investment of $10,000.
Answer:
The answer is: Following the expected value criterion the investor should choose indistinctively between the conservative or neutral alternatives.
Explanation:
The formula we use to calculate the expected return value of the different alternatives is:
ERV = ∑ (expected return x probability of occurrence)
The conservative alternative has an expected return value of of 4.5%
ERV Conservative = (6% x 25%) + (4% x 75%) = 4.5%
The neutral alternative also has an expected return value of of 4.5%
ERV Neutral = (12% x 25%) + (4% x 75%) = 4.5%
The aggressive alternative has an expected return value of of -1%
ERV Aggressive = (20% x 25%) + (-8% x 75%) = -1%