Explanation:
i=interest rate
X=current rate
2X = double current rate
n = number of years
Calculate time it takes to double at 3%:
2X = X(1+i)^n
simplify by cancelling out X
(1+i)^n = 2
substitute i = 3%
(1.03)^n =2
take log
n*log(1.03) = log(2)
n = log(2)/log(1.03) = 0.6931/0.02956 = 23.45 years
Similarly, for growth rate of 7%,
n = log(2)/log(1.07) = 0.6931 / 0.06766 = 10.24 years
So the difference is 23.45-10.24 = 13.21 years (to the hundredth) sooner
Answer:
$3,190
Explanation:
Incremental net income before tax = Incremental gross profit - Incremental SG&A expenses
= $5,000 - $400
= $4,600
Incremental net income after taxes = Incremental net income before tax * (1 - Tax rate)
Incremental net income after taxes = $4,600 * (1 - 0.35)
Incremental net income before tax = $4,600 * 0.65
Incremental net income before tax = $2990
Incremental cash flow = Incremental income after taxes + Depreciation
Incremental cash flow = $2,990 + $200
Incremental cash flow = $3,190
Answer:
Sharpe ratio = 0.20
Treynor ratio = –0.005
Explanation:
Note: See the attached excel file for the calculations of average rate of returns, standard deviations and beta used in the calculation below.
a. Calculation of Sharpe ratio
Sharpe ratio refers to a investment measurement that employed to measure the an investment actual that has been adjusted for the risk associated with the investment.
Sharpe ratio can be calculated using the following formula:
Sharpe ratio = (Average fund rate - Average Risk Free rate) / Standard deviation of fund rate = (5.46% - 2.40%) / 15.05% = 0.20
a. Calculation of Treynor ratio
Treynor ratio refers to investment measurement that is calculated to show the risk of certain investments after the volatility of the market has been taking into consideration.
Treynor ratio can be calculated using the following formula:
Treynor ratio = (Average market return rate - Average Risk Free rate) / Beta = (1.96% - 2.40%) / 87.53% = –0.005
Answer:
COGS= $5,910
Explanation:
Giving the following information:
Beginning inventory= 90 units at $19
Purchases 315 units at $20
Purchases 45 units at $22
Ending inventory= 150 units
First, we need to determine the number of units sold:
Units sold= 450 - 150= 300 units
Under the FIFO (first-in, first-out) method, the cost of goods sold is calculated using the cost of the first units incorporated:
COGS= 90*19 + 210*20= $5,910
Answer:
$9,760.48
Explanation:
Present value of annuity due = P* [[1 - (1+r)^-(n-1)] / r] + P. Where P = Periodic payment = $1,000, r = Rate of interest per period 4% (0.48/12), n = number of payments 12 (12*1)
Present value of annuity = $1000 * [[1 - (1 + 0.04)^-(12-1)] / 0.04] + $1000
Present value of annuity = $1000*8.760475 + $1000
Present value of annuity = $8760.48 + $1000
Present value of annuity = $9,760.48