Learning Module 2 Time Value of Money in Finance

You will receive EUR100,000 in 5 years. Using annual discrete compounding at 6 percent per year, what is the present value you should be willing to pay today?

A zero-coupon bond with face value USD1,000 matures in 10 years. If the annual YTM is 4 percent with annual compounding, what is its price today?

A 5-year bond pays annual coupons of 3 percent on par USD1,000 (i.e., USD30 annually) and returns principal at maturity. If market YTM is 4 percent, what is the bond price approximately?

You buy a perpetuity that pays USD50 per year forever and the appropriate discount rate is 5 percent. What is the price you should pay today?

A mortgage loan of EUR200,000 has a 30-year term and a quoted annual rate of 4.8 percent, paid monthly. What is the monthly payment approximately? (Use PV formula A = r_period * PV / (1 - (1 + r_period)^{-N})).

A stock currently trades at USD50 with expected D1 = USD2.00. If the market requires a return of 10 percent, what is the implied long-run P/E multiple using payout = D1/E1 where earnings E1 equals USD4.00 next year?

You observe a 2-year discount bond priced at USD95.72 with face USD100. What is the annual YTM?

A 7-year coupon bond pays annual coupons of 2 percent on EUR100 par. At issuance the YTM is 2 percent. What was the issue price per EUR100 and why?

An investor purchases a bond at issuance when YTM was −0.05 percent and sells after 6 years at a price implying a 1.10 percent annual YTM for the remaining 4 years. If initial PV was EUR100.50 and later price is EUR95.72, what was the investor's annualized return over the first six years?

A fund reports quarterly holdings values and experienced a cash inflow at the beginning of Q2. To calculate the annual time-weighted return for the year, which procedure is correct?

An investor bought 1 share at USD200 at t=0, bought 1 more share at USD225 at t=1, received USD5 dividend at t=1 (not reinvested), and sold both at USD235 at t=2 and received USD10 dividends total. Using money-weighted return (IRR), which set of net cash flows should be used (CF0, CF1, CF2)?

Which measure neutralizes the effect of investor cash inflows and outflows and is preferred to evaluate portfolio manager performance?

A bond with semiannual coupons has nominal annual coupon 6.70 percent and YTM 7.70 percent nominal. What periodic rate and number of periods should be used to price it for 20 years?

If an investor annuallyizes a monthly return of 0.8 percent, what annual return does she obtain (assume 12 months)?

What is the continuously compounded equivalent of a 4 percent holding-period return?

If a monthly quoted nominal rate is 6 percent (annual nominal with monthly compounding), what is the effective annual rate (EAR)?

Which of the following best describes the yield-to-maturity (YTM) of a bond?

A fund reports annual returns of 15%, -5%, 10%, 15%, and 3% over five years. What is the geometric mean annual return (approx)?

Which return measure is appropriate when comparing portfolio managers who face different client cash flow patterns but manage the same underlying investments?

You observe two one-year risk-free rates: r1 = 2.5% for one year and r2 = 3.5% for two years (annual). What is the implied one-year forward rate one year from now, F1,1 (annual)?

Covered interest parity under continuous compounding links forward FX F_{f/d}(T) to spot S_{f/d} and domestic/foreign continuously compounded rates r_dom and r_for. Which formula below is correct?

Walbright Fund had beginning value USD100m, gains USD10m (Jan–Apr), USD2m dividends reinvested, and new USD20m investment on 1 May. Ending market value at year end excluding dividends is USD140m and dividends in year-end cash USD2.64m. For computing money-weighted return using IRR on quarterly cash flows (4-month periods), what are the net cash flows at t=0, t=1, t=2, t=3 (in millions)?

If a stock's continuously compounded return for one week is r = ln(P1/P0) = 0.03922, what is the associated holding-period (simple) return R?

An investor requires at least 5 percent per year. Portfolio A has expected return 10% and standard deviation 15%; Portfolio B expected return 12% and SD 18%. Which portfolio has lower probability of falling below 5% under normality assumption (i.e., safety-first criterion)?

Compute the continuously compounded annual rate that is equivalent to an annual nominal rate of 6 percent (i.e., find r_cont where e^{r_cont} - 1 = 0.06).

A portfolio has beginning value USD1,000,000, receives USD200,000 at start of year 2, and ends with USD1,300,000. If the portfolio earned 10% in year 1, what is the time-weighted return for the year 1 to year 2 subperiod and how is it combined with other subperiod returns to get annual time-weighted return?

A bond price moves from 100 to 95.72 while a different investor buys at 95.72 and holds to maturity receiving 100 at maturity in 4 years. If the YTM for the 4-year hold at that time is 1.10% per year, what relationship ties the annualized returns across the entire 10-year original issue to the two holding segments (first 6 years and final 4 years)?

Using the constant growth dividend model, if P0 = 20, D1 = 1.2, compute implied r when g is assumed 2 percent.

A fund reports net-of-fees five-year holding period return of 42.35%. Manager disclosed fixed annual expenses of EUR0.5m when AUM was EUR30m in Year 1. How much did gross first-year return increase over net return due to adding back fixed expenses expressed in percentage points?

You observe S0 = USD40; in one period S_u = 56 and S_d = 32. A call option with strike X = 50 has payoffs Cu = 6, Cd = 0. Form a replicating portfolio with delta units of stock and borrowing/lending such that portfolio payoff is risk-free. What is delta?

Given the replicating portfolio in the prior question with delta = 0.25 and option payoffs Cu=6, Cd=0, the replicating portfolio values at t=1 in each state are 0.25*56 - 6 = 8 and 0.25*32 - 0 = 8. What is the present option price if risk-free discount factor for the period is 1/1.05 (r = 5%)?

Which of the following statements about gross and net returns is correct?

You observe a series of periodic returns: +15% and +6.67% for two consecutive years. What is the portfolio's time-weighted annual return?

A bond's price falls when market YTM rises. If a bond's price decreased by 4.78 after issuance, how will that affect an investor who bought at issuance and sold before maturity?

If a stock's next expected dividend is USD1.76 and price is USD63.00, and investors expect a required return of 7.00 percent, what is implied dividend growth g?

A 20-year bond with 6.70% annual coupon (paid semiannually) and YTM 7.70% (nominal) was priced at par at issuance. If the YTM immediately rises to 7.70%, the bond price falls. Which of the following is true about the bond's price change and remaining zero-coupon strip price (principal-only) for semiannual compounding?

Which of the following is true about the relationship between arithmetic and geometric means for periodic returns when variance is nonzero?

If an investor wants to compare returns reported over different holding periods (e.g., 100 days vs 4 weeks vs 3 months), what is the standard approach to make them comparable?

Which statement correctly explains why lognormal distribution is commonly used for modeling asset prices when returns are assumed normal under continuous compounding?

You simulate 1,000 yearly continuously compounded returns r_i ~ N(0.07, 0.12^2). For each r_i you compute future price S1_i = S0 * exp(r_i) with S0=1. Which distribution should you fit to the simulated S1_i values and why?

Monte Carlo simulation is most useful in which of the following investment valuation contexts?

What is the primary idea behind bootstrap resampling when used to model returns in a simulation?

Which method preserves empirical distributional features like skewness and kurtosis without imposing a parametric distribution in a simulation?

A money-market instrument quoted with continuous compounding has r_dom = 2.67% and foreign r_for = 1.562% for one-year. Spot USD/GBP = 1.2602 USD per GBP. What happens to the 1-year forward USD/GBP rate if r_dom increases more than r_for increase?

Suppose an investor requires at least RL = 3.75% to avoid invading principal next year. Allocation A: E(R)=25% σ=27%; Allocation B: E(R)=11% σ=8%; Allocation C: E(R)=14% σ=20%. Which allocation is safety-first optimal?

Which of these is a correct interpretation of YTM for a coupon bond?

Which of the following best explains why the geometric mean annual return is typically less than the arithmetic mean annual return for investment returns with volatility?