dr|ft

for the first one would it be

PV=1000

NP=1000

n=6

I=5.3189% pa (the pa value of 5.25% compounding semi-anually)

making the first question

Rd = [5.3189+ (1000 -1000)/6] / [(1000+1000)/2]

= 0.53189%

0.53189% x (1-0.36) = 0.3404096%

I didn't think these 2 questions applied to the other sub-forums so i put them in here.

So Rd = [ I + (PV-NP)/n] / [(PV+NP)/2]

where Rd = cost of debt

I = annual interest payment

PV = par (or face) value of the debenture

NP = net proceeds of the issue = market price less costs

n = the number of years to maturity of the debenture

Eg the book gives me is...

Suppose the Russ Saving Company issued an eight-year, 7 per cent debenture two years ago. The debenture is currently selling for $95.38. What is Russ Saving's cost of debt?

Rd = [7 + (100-95.38)/6] / [(100+95.38)/2]

= 7.95%

If we assume a corporate tax rate of 30 per cent this approximate rate is adjusted for tax as follows -

7.95% x (1-0.3) = 5.565%

OK that is straight from the text also "The cost of debt is the return that the firm's debtholder demand on new borrowing" if u were wondering.

Find the cost of debt capital for Danny's Dangerous Didgeridoos if they issued corporate bonds with a face value of $1,000, paying interest at 5.25% pa compounded semi-annually, with a maturity of exactly 6 years. The current price is $1,000. The corporate tax rate is 36%. You may give your answer as an after-tax percentage per annum to the nearest percent or use linear interpolation or a financial calculator to give a more accurate result. Your answer should remain compounded semi-annually.

Cost of debt = % pa

A $1,000 corporate bond, issued by Ellie's Elegant Eveningwear, paying half-yearly compounding interest at 5.25% matures on 24 July 2013. If this corporate bond is worth $1,030.68 on 24 July 2006, what is the cost of debt, compounded semi-annually, for Ellie's Elegant Eveningwear? The corporate tax rate is 38%. You may give your answer as an after-tax percentage per annum to the nearest percent or use linear interpolation or a financial calculator to give a more accurate result.

Cost of debt = % pa

If you guys could give me a hand that would be awesome, thanks.

thanks a lot i got it all figured

ahh it must be cone inside a sphere then, thanks for that

A sphere of radius 8 cm is circumscribed by a right circular cone. If the cone is to have a max volume, find the height of the cone and the radius of the base of teh cone...

I need to relate the radius of the sphere to either the radius of the base or height of the cone, i can't find anything, any ideas people?

Vol of Sphere = 4/3 TTr^3

Vol of Cone = 1/3 .TT.r^2.h

you got 54.7356 degrees? cool. My question also asks me to 'theoretically' prove that theta produces a minimum value using the 'first derivative test', is that what we've already done or is there more to it?

Wait my quesiton only wanted me to find Surface Area with respect to s and h so i just go back to the original equation and sub in 54.7356 for theta, is that what you guys got?

Is my next step to go back to A' = 1.5s^2 csc^2 X - 1.5root(3)s^2 csc X . cot X

let A=0, X=54.7356 and solve for s... so it would be

0 = 1.5s^2csc^254.7356 - 1.5root(3)s^2.csc54.7356

hmmm that doesn't look right it seems the s' will cancel out

can't i cancel csc because its csc^2X / cscX.cotX = root(3)

which is the same as

cosecX/cosecX * cosecX/cotX = root(3) ?

EDIT:

If i solve secX=root(3) X comes out to be 0.99 or something which couldn't possibly be correct

DOUBLE EDIT:

Wait no i put it in as 1/cosX=root(3) and it came out as 54.7356 again

yeah that's right DQW, it's [3.root(3).s^2]/[2sinX]....so now i have

0=1.5s^2.csc^2X - 1.5root(3).s^2.cscX.cotX and i want to find X....

I would start by splitting the equation to look like

1.5s^2.csc^2X = 1.5root(3).s^2.cscX.cotX

divide both sides by 1.5 and s^2

csc^2X = root(3)cscX.cotX

seperate the X's by dividing RHS by cscX.cotX

csc^2X / cscX.cotX = root(3)

cancel the csc's leaving

cosecX / cotX = root(3)

hmmmmmmm hit a wall

EDIT:

I can plug tanX/sinX = root(3) in my graphics calc and solve for X to get 54.7356 which seems OK..... btw i got tanX/sinX by going cosecX = 1/sinX and cotX = 1/tanX. Anyone have any ideas for manually equating?

So we want to derive A = 6sh -1.5s^2 cot X + ((3 square root 3s^2)/2sinX)....

6sh would go to 0.... -1.5s^2 cotX would go to... derivative of cotX is -csc^2 X so it goes to 1.5x^2csc^2 X

((3 square root 3s^2)/2sinX) would go to - 1.5rt3s^2 csc X . cot X ???

making it..

A' = 1.5s^2 csc^2 X - 1.5root3s^2 csc X . cot X

????

EDIT

checking that last bit of the equation on maple

> diff((3*sqrt(3*s^2))/(2*sin(x)),x);

3 .root(3).root(s^2).cos(x)

- -------------------------

2 sin(x)^2

I'm assuming this is correct, if so could someone please show me the steps in getting that

EDIT:

ok for the last bit ((3 square root 3s^2)/2sinX) i think you use the quotient rule so lets call 3sqrt(3s^2) 'f' and 2sinX 'g' ..... the rule is g.[df/dx] - f.[dg/dx] all over g^2

so that will equate to [2sinX.0 - 3sqrt(3s^2).2cosX] / 4sin^2X

or (-3sqrt(3s^2).2cosX)/(4sin^2X)

=] deriving then letting A = 0 ? somethign along those lines

In a beehive, each cell is a regular prism, open at one end with a trihedral angle at the other end, it is believed that bees form their cells in such a way as to minimize the surface area for a given volume, thus using the least amount of wax in cell construction examination of these cells has shown that the measure of the apex angle is amazingly consistent based on the geometry of the cell, it can be shown that the surface area is given by A = 6sh -1.5s^2 cot X + ((3 square root 3s^2)/2sinX) where s is the length of sides of the hexagon and h is the height , and they are constants.

Use the optimisation theory to determine the minimum surface area of the cell in terms of s and h, verify the answer by sketching the Surface A function on graphmatica for spec values of s and h. ( these values may be arbitarily chosen) use the first derivative test to theoretically prove that X produces a min value.

Thx

determine if the following sets of vectors are vector spaces:

V = {(x y z) from R^3 | ax + by + cz = 0, a, b, c from reals and not all 0}

Help would be much appreciated

i THINK i remember the answer being in the 82's actually, that looks like a good solution mezarashi i gotta analyze it, thanks for the help tho

if its a solution, i guess post it? dave was using that idea i think he is solving it that way and posting the solution shortly

Ok i've attatched the shapes. Now what that is, is a square with 4 1/4 circles going through it. The aim is to find the shaded area and we know that the sides of the square are 10cm. Good Luck.

find derivate of root (2x - 1) using first principles, Thanks for your help.