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Math Help - Investing Fundamentals

  1. #1
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    Investing Fundamentals

    John recently won a large sum of money which will be disbursed through two alternative payments:


    • Option 1: A one off payment of RM100,000 that will be paid in 10 years.
    • Option 2: Three uneven payments of RM10,000, RM30,000 and RM40,000 that will be paid in year 1, 5 and 10, respectively.


    Assuming that the current market interest rate is 8 percent, which alternative would John choose?
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  2. #2
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    Re: Investing Fundamentals

    Quote Originally Posted by mastermin346 View Post
    John recently won a large sum of money which will be disbursed through two alternative payments:


    • Option 1: A one off payment of RM100,000 that will be paid in 10 years.
    • Option 2: Three uneven payments of RM10,000, RM30,000 and RM40,000 that will be paid in year 1, 5 and 10, respectively.


    Assuming that the current market interest rate is 8 percent, which alternative would John choose?
    FV - future value
    PV - present value
    r - interest rate
    t - time
    FV = PV(1+r)t

    the value of option 1 in 10 years is $100,000

    to find the value of option 2 we assume he invests all payments at 8% as soon as he receives them

    FV = $10000(1.08)(10-1) + $30000(1.08)(10-5) + $40000 = $19990.045 + $44079.84 + $40000 = $104069.89

    option two has a larger overall future value than option 1.
    Thanks from mastermin346 and arrianewright
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  3. #3
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    Re: Investing Fundamentals

    That was cool romsek. Thanks! This is a pretty tough problem, but you got it right. By the way, since we're talking about investments in here, you can check out here if you want to read more financial blogs and articles which may help you create mathematical problems.
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    Re: Investing Fundamentals

    is that what you are? a spammer? just what we need more of....
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    Re: Investing Fundamentals

    The other answer did the comparison of net future value of both investments at time period t = 10

    That means how much each of the investments is worth at maturity

    One may also get the same results by checking how much each of the investment is worth at present time period t=0

    The comparison can then be made between the two present values to confirm that indeed the second investment is worth more than the first

    PV = 100000 x (1+8%)^-10
    PV = 100000 x 0.46319
    PV = 46,319.35

    Code:
    T    CF x PVIF           CF x PVIF         Present Value
    1    10000 x (1+8%)^-1   10000 x 0.92593   9,259.26
    5    30000 x (1+8%)^-5   30000 x 0.68058   20,417.50
    10   40000 x (1+8%)^-10   40000 x 0.46319  18,527.74
                                          NPV  $48,204.49
    You can also find the future value of the investment by compounding the calculated net present value of 48,204.49 by a discount factor of (1+8%)^10 or 1.08^10

    NFV = 48,204.49 x 1.08^10
    NFV = 48,204.49 x 2.15892499727278669824
    NFV = 104,069.89
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  6. #6
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    Re: Investing Fundamentals

    Investments may be held till maturity or they may be disposed off at an intermediate date between commencement of payments and terminal payment

    Thus to evaluate an investment other than finding present and future worth of such an investment, an investor would also be interested in finding an intermediate net value of such an investment

    For example, what if you decided to sell this investment at time period t=5, you would be keen to find the net value of such an investment at such time period.

    Here is how

    Code:
    T	C		factor		c x factor		Intermediate Value
    5	100,000		(10.8)^-5	100,000 x 0.680583197	68,058.32
    
    T	C		factor		c x factor		Intermediate Value
    5	10,000		(1.08)^4	10,000 x 1.36048896	13,604.89
    5	30,000		1		30,000 x 1		30,000
    5	40,000		(10.8)^-5	40,000 x 0.680583197	27223.33
    					Net intermediate value  70,828.22
    Even if did want to dispose of the investment at time period t=5, the second investment is worth more than the first as the 100,000 due at t=10 is only worth 68,058.32 and the three payments from the second investment at t=5 are worth more as in 70,828.22
    Last edited by AbrahamA; April 12th 2014 at 08:44 PM. Reason: edited the time period
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  7. #7
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    Re: Investing Fundamentals

    Once we have the NIV - net intermediate value, we can confirm the NFV - net future value as shown in the other reply and the NPV - net present value as shown in the second last reply

    To find NPV from NIV, we shall discount it by 5 years at 8%

    Code:
    NIV		factor		factor		NIV x factor			NPV
    70,828.22	(1.08)^-5	0.680583197	70,828.22 x 0.680583197		48,204.49
    To find NFV from NIV, we shall compound it by 5 years at 8%

    Code:
    NIV		factor		factor		NIV x factor			NFV
    70,828.22	(1.08)^5	1.4693280768	70,828.22 x 1.4693280768	104,069.89
    An NIV may be found for any time period between t=0 and t=N. The most useful examples of such intermediate values would be for the 1st qaurtile, 2nd quartile, and 3rd quartile NIV values.

    The NIV is more useful of a measure as compared to NPV or NFV as we may be interested in finding the time period at which the investment yields the maximum NIV that may be totally different from the NFV or NPV for the full horizon of the investment.
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  8. #8
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    Re: Investing Fundamentals

    Quote Originally Posted by mastermin346 View Post
    John recently won a large sum of money which will be disbursed through two alternative payments:


    • Option 1: A one off payment of RM100,000 that will be paid in 10 years.
    • Option 2: Three uneven payments of RM10,000, RM30,000 and RM40,000 that will be paid in year 1, 5 and 10, respectively.


    Assuming that the current market interest rate is 8 percent, which alternative would John choose?
    Here's how I would do this problem, not having any real knowledge of "financial formulas":

    The RM10,000 that he gets "in year 1" can be invested, at 8% interest, for 10 years (I assume compounded annually) and so will be worth 10000(1.08)^{10}= 21589.26 at the end of the 10 years. The RM30,000 that he gets "in year 5" can be invested at 8% interest for 5 years and so will be worth 30000(1.08)^{5}= 44079.84 at the end of the 10 years. That, added to the RM40,000 he gets "in year 10" makes a total of 21,589.26+ 44,079.94+ 40,000= RM105669.10 which is MORE than RM100,000 at the end of 10 years.
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