Answer:
The correct answer is $23,663
Explanation:
Spreadsheet is attached with the calculus.
Depreciation expense is the difference between the cost of the asset and the residual value, divided by the useful life of the asset.
Depreciation expense=(original cost-residual cost) /useful life
In this case, conditions change at third year. First, we must calculate the depreciation expense with the first situation. The first 2 years , we are going to decrease the asset value with this depreciation expense.
Situation 1 Depreciation expense 14375
At third year , we must recalculate the depreciation expense. The final value of second years is the new "original value".
Situation 2
Original Value 97250
Residual Value 2600
Useful life 4
Depreciation expense= (97250
- 2600
)/4
Depreciation expense= 23,663
The applicable formula is;
A = P(1-r)^n
Where;
A = Final purchasing power
P = Current purchasing power
r = inflation
n = Number of years when P changes to A
Confirming the first claim:
A = 1/2P (to be confirmed)
P = $3
r = 7% = 0.07
n = 10.25 years
Using the formula;
A = 3(1-0.07)^10.25 = 3(0.475) ≈ 3(0.5) = $1.5
And therefore, A = 1/2P after 10.25 years.
Now, give;
P = $9
A = 1/4P = $9/4 = $2.25
r = 6.5% = 0.065
n = ? (nearest year).
Substituting;
2.25 = 9(1-0.065)^n
2.25/9 = (1-0.065)^n
0.25 = (1-0.065)^n
ln (0.25)= n ln(1-0.065)
-1.3863 = -0.0672n
n = (-1.3863)/(-0.0672) = 20.63 years
To nearest year;
n = 21 years
Therefore, it would take approximately 21 years fro purchasing power to reduce by 4. That is, from $9 to $2.25.
Answer:
The market price of this bond is: $1,069.8.
Explanation:
To calculate the market price of the bond, we have to use the following formula:
Bond Price= C*((1-(1+r)^-n)/r)+(F/(1+r)^n)
C= periodic coupon payments: $1,000*7%= $70
F= Face value: $1,000
r= Yield to maturity: 5.85%
n= No. of periods until maturity: 8 years
Bond Price= 70*((1-(1+0.0585)^-8)/0.0585)+(1,000/(1+0.0585)^8)
Bond Price= 70*((1-0.635)/0.0585)+(1,000/1.58)
Bond Price= 70*6.24+633
Bond Price= 436.8+633
Bond Price= 1,069.8
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