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Darya [45]
3 years ago
5

You have entered into a long forward contract on a dividend-paying stock some time ago, and this will expire in six months. It h

as a delivery price of $40 and the current stock price is $35. The stock provides a fixed dividend yield of 8% with semi-annual compounding. If the risk-free rate is 12% per annum with continuous compounding, what is the value of this long forward contract?
A. $6.72

B. -$4.02

C. $4.02

D. -$6.72
Business
1 answer:
Vlad1618 [11]3 years ago
5 0

Answer:

correct option is B. -$4.02

Explanation:

given data

delivery price = $40

current stock price = $35

fixed dividend yield = 8% = 0.08

risk free rate = 12% = 0.12

solution

as we know that forward contract is a agreement that is made between 2 parties ( seller or buyer ) asset in future at today fix price in specified time,

we get here long forward contract value that is express as

long forward contract = \frac{stock\ price}{(1+dividend\ rate)^t} -\frac{forward\ rate}{e^{r*t}}    ...................1

put here value we get

long forward contract = \frac{35}{(1+0.08)^{6/12}} -\frac{40}{e^{0.12*6/12}}  

solve it we get

long forward contract = -$4.02

so correct option is B. -$4.02

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A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by upper c equals 0.
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Answer:

The cost per month is increasing at a rate $365.

Explanation:

Differentiation Formula

  • \frac{d}{dx}(x^n)= nx^{n-1}  
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A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month is given by

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Again given that,

the rate of changing production is 13 unit per month

i.e \frac{dx}{dt}=13

To find the cost per month, we need to find out the value \frac{dc}{dt} when production is changing at the rate 13 units per month and the production is 70 units.

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Differentiating with respect to t

\frac{d}{dt}(c)=\frac{d}{dt}(0.2x^2)+\frac{d}{dx}(10,000)

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\Rightarrow \frac{dc}{dt}=0.2\times 2x^{2-1}\frac{dx}{dt}+0

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Plugging \frac{dx}{dt}=13

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